scholarly journals Completeness of b−Metric Spaces and Best Proximity Points of Nonself Quasi-Contractions

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2206
Author(s):  
Arshad Ali Khan ◽  
Basit Ali
Keyword(s):  
Symmetric Spaces ◽  
Metric Spaces ◽  
The Other ◽  
Best Proximity Points

The aims of this article are twofold. One is to prove some results regarding the existence of best proximity points of multivalued non-self quasi-contractions of b−metric spaces (which are symmetric spaces) and the other is to obtain a characterization of completeness of b−metric spaces via the existence of best proximity points of non-self quasi-contractions. Further, we pose some questions related to the findings in the paper. An example is provided to illustrate the main result. The results obtained herein improve some well known results in the literature.

scholarly journals ON THE DEFINITIONS OF SOBOLEV AND BV SPACES INTO SINGULAR SPACES AND THE TRACE PROBLEM

2007 ◽  
Vol 09 (04) ◽  
pp. 473-513 ◽  
Author(s):  
DAVID CHIRON
Keyword(s):  
Sobolev Spaces ◽  
Metric Spaces ◽  
The Other ◽  
Dirichlet Energy ◽  
Singular Spaces ◽  
Other Hand ◽  
The One

The purpose of this paper is to relate two notions of Sobolev and BV spaces into metric spaces, due to Korevaar and Schoen on the one hand, and Jost on the other hand. We prove that these two notions coincide and define the same p-energies. We review also other definitions, due to Ambrosio (for BV maps into metric spaces), Reshetnyak and finally to the notion of Newtonian–Sobolev spaces. These last approaches define the same Sobolev (or BV) spaces, but with a different energy, which does not extend the standard Dirichlet energy. We also prove a characterization of Sobolev spaces in the spirit of Bourgain, Brezis and Mironescu in terms of "limit" of the space Ws,p as s → 1, 0 < s < 1, and finally following the approach proposed by Nguyen. We also establish the [Formula: see text] regularity of traces of maps in Ws,p (0 < s ≤ 1 < sp).

scholarly journals Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Manuel De la Sen ◽  
Erdal Karapınar
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Convex Banach Space ◽  
Probabilistic Metric Spaces ◽  
Best Proximity Points ◽  
Menger Spaces ◽  
Cyclic Contractions ◽  
Probabilistic Metric

This paper investigates properties of convergence of distances ofp-cyclic contractions on the union of thepsubsets of an abstract setXdefining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of Cauchy sequences which converge to the best proximity points. The existence and uniqueness of fixed points and best proximity points ofp-cyclic contractions defined in induced complete Menger spaces are also discussed in the case when the associate complete metric space is a uniformly convex Banach space. On the other hand, the existence and the uniqueness of fixed points of thep-composite mappings restricted to each of thepsubsets in the cyclic disposal are also investigated and some illustrative examples are given.

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.

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.

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 An Intrinsic Characterization of Five Points in a CAT(0) Space

2020 ◽  
Vol 8 (1) ◽  
pp. 114-165
Author(s):  
Tetsu Toyoda
Keyword(s):  
Metric Space ◽  
Isometric Embedding ◽  
Metric Spaces ◽  
Necessary Conditions ◽  
New Approach ◽  
Intrinsic Characterization ◽  
New Family

AbstractGromov (2001) and Sturm (2003) proved that any four points in a CAT(0) space satisfy a certain family of inequalities. We call those inequalities the ⊠-inequalities, following the notation used by Gromov. In this paper, we prove that a metric space X containing at most five points admits an isometric embedding into a CAT(0) space if and only if any four points in X satisfy the ⊠-inequalities. To prove this, we introduce a new family of necessary conditions for a metric space to admit an isometric embedding into a CAT(0) space by modifying and generalizing Gromov’s cycle conditions. Furthermore, we prove that if a metric space satisfies all those necessary conditions, then it admits an isometric embedding into a CAT(0) space. This work presents a new approach to characterizing those metric spaces that admit an isometric embedding into a CAT(0) space.

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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