scholarly journals Chordality Properties and Hyperbolicity on Graphs

10.37236/5315 ◽  
2016 ◽  
Vol 23 (3) ◽  
Author(s):  
Álvaro Martínez-Pérez
Keyword(s):  
Shortest Path ◽  
The Other ◽  
Geodesic Triangle ◽  
Two Sides

Let $G$ be a graph with the usual shortest-path metric. A graph is $\delta$-hyperbolic if for every geodesic triangle $T$, any side of $T$ is contained in a $\delta$-neighborhood of the union of the other two sides. A graph is chordal if every induced cycle has at most three edges. In this paper we study the relation between the hyperbolicity of the graph and some chordality properties which are natural generalizations of being chordal. We find chordality properties that are weaker and stronger than being $\delta$-hyperbolic. Moreover, we obtain a characterization of being hyperbolic on terms of a chordality property on the triangles.

scholarly journals Distortion of the Hyperbolicity Constant of a Graph

10.37236/2175 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Walter Carballosa ◽  
Domingo Pestana ◽  
José M. Rodríguez ◽  
José M. Sigarreta
Keyword(s):  
Metric Space ◽  
Quantitative Information ◽  
The Other ◽  
Geodesic Triangle ◽  
Interesting Topic ◽  
Geodesic Metric Space ◽  
Geodesic Metric ◽  
Hyperbolic Graphs ◽  
Two Sides ◽  
Hyperbolicity Constant

If $X$ is a geodesic metric space and $x_1,x_2,x_3\in X$, a geodesic triangle $T=\{x_1,x_2,x_3\}$ is the union of the three geodesics $[x_1x_2]$, $[x_2x_3]$ and $[x_3x_1]$ in $X$. The space $X$ is $\delta$-hyperbolic $($in the Gromov sense$)$ if any side of $T$ is contained in a $\delta$-neighborhood of the union of the other two sides, for every geodesic triangle $T$ in $X$. We denote by $\delta(X)$ the sharp hyperbolicity constant of $X$, i.e., $\delta(X):=\inf\{\delta\ge 0: \, X \, \text{ is $\delta$-hyperbolic}\,\}$. The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it. One of the main aims of this paper is to obtain quantitative information about the distortion of the hyperbolicity constant of the graph $G\setminus e$ obtained from the graph $G$ by deleting an arbitrary edge $e$ from it. These inequalities allow to obtain the other main result of this paper, which characterizes in a quantitative way the hyperbolicity of any graph in terms of local hyperbolicity.

A very rapid in situ Kikuchi technique to determine relative crystal misorientation

1988 ◽  
Vol 46 ◽  
pp. 830-831
Author(s):  
J. I. Bennetch
Keyword(s):  
Electron Beam ◽  
Analytical Techniques ◽  
Superplastic Forming ◽  
The Other ◽  
Kikuchi Pattern ◽  
Kikuchi Line ◽  
Line Analysis

In a recent study of the superplastic forming (SPF) behavior of certain Al-Li-X alloys, the relative misorientation between adjacent (sub)grains proved to be an important parameter. It is well established that the most accurate way to determine misorientation across boundaries is by Kikuchi line analysis. However, the SPF study required the characterization of a large number of (sub)grains in each sample to be statistically meaningful, a very time-consuming task even for comparatively rapid Kikuchi analytical techniques.In order to circumvent this problem, an alternate, even more rapid in-situ Kikuchi technique was devised, eliminating the need for the developing of negatives and any subsequent measurements on photographic plates. All that is required is a double tilt low backlash goniometer capable of tilting ± 45° in one axis and ± 30° in the other axis. The procedure is as follows. While viewing the microscope screen, one merely tilts the specimen until a standard recognizable reference Kikuchi pattern is centered, making sure, at the same time, that the focused electron beam remains on the (sub)grain in question.

Characterization of defects in tabular silver halide grains

1990 ◽  
Vol 48 (4) ◽  
pp. 1046-1047
Author(s):  
C. Goessens ◽  
D. Schryvers ◽  
J. Van Landuyt ◽  
A. Verbeeck ◽  
R. De Keyzer
Keyword(s):  
Radiation Damage ◽  
Silver Halide ◽  
Chemical Characteristics ◽  
X Ray ◽  
Free Region ◽  
Central Defect ◽  
Crystallographic Defects ◽  
Physical And Chemical ◽  
Two Sides

Silver halide grains (AgX, X=Cl,Br,I) are commonly recognized as important entities in photographic applications. Depending on the preparation specifications one can grow cubic, octahedral, tabular a.o. morphologies, each with its own physical and chemical characteristics. In the present study crystallographic defects introduced by the mixing of 5-20% iodide in a growing AgBr tabular grain are investigated. X-ray diffractometry reveals the existence of a homogeneous Ag(Br1-xIx) region, expected to be formed around the AgBr kernel. In fig. 1 a two-beam BF image, taken at T≈100 K to diminish radiation damage, of a triangular tabular grain is presented, clearly showing defect contrast fringes along four of the six directions; the remaining two sides show similar contrast under relevant diffraction conditions. The width of the central defect free region corresponds with the pure AgBr kernel grown before the mixing with I. The thickness of a given grain lies between 0.15 and 0.3 μm: as indicated in fig. 2 triangular (resp. hexagonal) grains exhibit an uneven (resp. even) number of twin interfaces (i.e., between + and - twin variants) parallel with the (111) surfaces. The thickness of the grains and the existence of the twin variants was confirmed from CTEM images of perpendicular cuts.

Rapid Isolation of High Molecular Weight Urokinase from Native Human Urine

1982 ◽  
Vol 47 (03) ◽  
pp. 197-202 ◽  
Author(s):  
Kurt Huber ◽  
Johannes Kirchheimer ◽  
Bernd R Binder
Keyword(s):  
Molecular Weight ◽  
High Molecular Weight ◽  
Human Urine ◽  
Gel Filtration ◽  
Chain Structure ◽  
The Other ◽  
Single Chain ◽  
Apparent Homogeneity ◽  
Sequential Adsorption

SummaryUrokinase (UK) could be purified to apparent homogeneity starting from crude urine by sequential adsorption and elution of the enzyme to gelatine-Sepharose and agmatine-Sepharose followed by gel filtration on Sephadex G-150. The purified product exhibited characteristics of the high molecular weight urokinase (HMW-UK) but did contain two distinct entities, one of which exhibited a two chain structure as reported for the HMW-UK while the other one exhibited an apparent single chain structure. The purification described is rapid and simple and results in an enzyme with probably no major alterations. Yields are high enough to obtain purified enzymes for characterization of UK from individual donors.

Eurasian "Theory of Economy Management" as an Organic Part of the Russian Economic School

2003 ◽  
pp. 95-110
Author(s):  
M. Voeykov
Keyword(s):  
Economic Development ◽  
Theoretical Model ◽  
Initial Step ◽  
State Regulation ◽  
Soviet Economy ◽  
The Other ◽  
Large Share ◽  
Organic Part ◽  
Two Sides ◽  
Enterprise Activity

The original version of "the theory of economy management", developed in the 1920s by Russian economists-emigrants who called themselves "Eurasians" (N. Trubetskoy, P. Savitskiy, etc.) is analyzed in the article. They considered this theory to be the basis of the original Russia's way of economic development. The Eurasian theory of economy management focuses on two sides of enterprise activity: managerial as well as social and moral. The Eurasians accepted the Soviet economy with the large share of state regulation as the initial step of development. On the other hand they paid much attention to the private sector activity. Eurasians developed a theoretical model of the mixed economy which can be attributed as the Russian economic school.

The Other Side Of The Coin: An Enquiry Into The Difficulties And Apprehensions Encountered By Consumers With Green Products

2019 ◽  
Vol 118 (8) ◽  
pp. 152-159
Author(s):  
Jijimon M J ◽  
Dr. S. Anthony Rahul Golden ◽  
Dr. S. Bulomine Regi
Keyword(s):  
The Other ◽  
Green Products ◽  
Two Sides

Every reality has its own positives and negatives. As the proverb goes coin has two sides. It is very much true in the case of green products too. There is no doubt that green products have many benefits and positives. Despite all the good things about green products, there exist a few glitches and shadows, thereby creating a few doubts and apprehensions in the minds of consumers. The present paper tries to understand these problems associated with green products from the perspectives of the consumers and analyses them with an intention of providing the green brands the means and ways to eliminate such anomalies. The study finds out that the unavailability of products is the most difficult thing the consumers have experienced while purchasing.

scholarly journals Analysis of the Mechanism by Which Glucose Inhibits Maltose Induction of MAL Gene Expression in Saccharomyces

Genetics ◽  
2000 ◽  
Vol 154 (1) ◽  
pp. 121-132
Author(s):  
Zhen Hu ◽  
Yingzi Yue ◽  
Hua Jiang ◽  
Bin Zhang ◽  
Peter W Sherwood ◽  
...  
Keyword(s):  
Gene Expression ◽  
Glucose Repression ◽  
Protein A ◽  
The Other ◽  
Maltose Permease ◽  
Inducer Exclusion ◽  
Glucose Inhibition ◽  
Independent Mechanism ◽  
Mal Genes

Abstract Expression of the MAL genes required for maltose fermentation in Saccharomyces cerevisiae is induced by maltose and repressed by glucose. Maltose-inducible regulation requires maltose permease and the MAL-activator protein, a DNA-binding transcription factor encoded by MAL63 and its homologues at the other MAL loci. Previously, we showed that the Mig1 repressor mediates glucose repression of MAL gene expression. Glucose also blocks MAL-activator-mediated maltose induction through a Mig1p-independent mechanism that we refer to as glucose inhibition. Here we report the characterization of this process. Our results indicate that glucose inhibition is also Mig2p independent. Moreover, we show that neither overexpression of the MAL-activator nor elimination of inducer exclusion is sufficient to relieve glucose inhibition, suggesting that glucose acts to inhibit induction by affecting maltose sensing and/or signaling. The glucose inhibition pathway requires HXK2, REG1, and GSF1 and appears to overlap upstream with the glucose repression pathway. The likely target of glucose inhibition is Snf1 protein kinase. Evidence is presented indicating that, in addition to its role in the inactivation of Mig1p, Snf1p is required post-transcriptionally for the synthesis of maltose permease whose function is essential for maltose induction.

scholarly journals On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 116
Author(s):  
Qi Liu ◽  
Yongjin Li
Keyword(s):  
Banach Spaces ◽  
Product Space ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
The Other ◽  
Inner Product ◽  
Equivalent Characterization ◽  
Geometric Constant ◽  
Geometric Constants

In this paper, we will introduce a new geometric constant LYJ(λ,μ,X) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.

The development of body and organ shape

BMC Zoology ◽  
2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Ansa E. Cobham ◽  
Christen K. Mirth
Keyword(s):  
Relative Position ◽  
Body Shape ◽  
Single Cells ◽  
The Other ◽  
Geometric Features ◽  
Main Text ◽  
Size Characterization ◽  
Organ Shape ◽  
The Many

Abstract Background Organisms show an incredibly diverse array of body and organ shapes that are both unique to their taxon and important for adapting to their environment. Achieving these specific shapes involves coordinating the many processes that transform single cells into complex organs, and regulating their growth so that they can function within a fully-formed body. Main text Conceptually, body and organ shape can be separated in two categories, although in practice these categories need not be mutually exclusive. Body shape results from the extent to which organs, or parts of organs, grow relative to each other. The patterns of relative organ size are characterized using allometry. Organ shape, on the other hand, is defined as the geometric features of an organ’s component parts excluding its size. Characterization of organ shape is frequently described by the relative position of homologous features, known as landmarks, distributed throughout the organ. These descriptions fall into the domain of geometric morphometrics. Conclusion In this review, we discuss the methods of characterizing body and organ shape, the developmental programs thought to underlie each, highlight when and how the mechanisms regulating body and organ shape might overlap, and provide our perspective on future avenues of research.

scholarly journals Development of a New Pasta Product by the Incorporation of Chestnut Flour and Bee Pollen

2021 ◽  
Vol 11 (14) ◽  
pp. 6617
Author(s):  
Maëlys Brochard ◽  
Paula Correia ◽  
Maria João Barroca ◽  
Raquel P. F. Guiné
Keyword(s):  
Wheat Flour ◽  
Nutritional Composition ◽  
Cooking Time ◽  
The Other ◽  
Physical Characterization ◽  
Chemical Analyses ◽  
High Fiber ◽  
Chestnut Flour ◽  
Cooking Yield

This work aimed at developing fortified pastas incorporating chestnut flour (25–55%) and powdered pollen (5–20%), either separately or in combination, as well as the characterization of the products obtained. To this, a physical characterization was carried out (analyzing texture and color), complemented with chemical analyses to determine the nutritional composition. Results showed that adding chestnut flour over 40% to wheat-flour pasta shortened optimum cooking time and lowered cooking yield, and the addition to pasta prepared with wheat flour and eggs maintained approximately constant the cooking yield. Additionally, the incorporation of pollen powder (up to 20%) in pasta prepared with wheat flour and water or fresh egg shortened the cooking time and cooking yield, in both fresh and dried pasta. The most suitable percentages of the new ingredients were 50% for chestnut and 10% for pollen. Comparing with the control pasta recipe (wheat flour and egg), the addition of chestnut flour (50%) or pollen powder (10%) increased stickiness, adhesiveness and the darkening of the final product (fresh or dried) but maintained the firmness of the pasta. The cooking of fresh or dried pasta enriched with both ingredients turned the pasta clearer and slightly stickier. On the other hand, the addition of chestnut flour and pollen powder in pasta formulation delivered a nutritionally balanced product with high fiber, vitamins and minerals. Overall, chestnut flour and powdered pollen represent promising ingredients for the development of functional fresh and dried pasta formulations.

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