The difference of \chi^2 over p-metric spaces defined by Musielak

2013 ◽  
Vol 7 ◽  
pp. 4081-4095
Author(s):  
N. Kavitha ◽  
N. Saivaraju ◽  
N. Subramanian
Keyword(s):  
Author(s):  
Richard Earl

Most functions have several numerical inputs and produce more than one numerical output. But even generally continuity requires that we can constrain the difference in outputs by suitably constraining the difference in inputs. ‘The plane and other spaces’ asks more general questions such as ‘is the distance a car has travelled a continuous function of its speed?’ This is a subtle question as neither the input nor output are numbers, but rather functions of time, with input the speed function s(t) and output the distance function d(t). In answering the question, it considers continuity between metric spaces, equivalent metrics, open sets, convergence, and compactness and connectedness, the last two being topological invariants that can be used to differentiate between spaces.


2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Mujahid Abbas ◽  
Maher Berzig

We establish fixed-point theorems for mixed monotone mappings in the setting of ordered metric spaces which satisfy a contractive condition for all points that are related by a given ordering. We also give a global attractivity result for all solutions of the difference equation where satisfies certain monotonicity conditions with respect to the given ordering. As an application of our obtained results, we present some iterative algorithms to solve a class of matrix equations. A numerical example is also presented to test the validity of the algorithms.


2014 ◽  
Vol 33 (1) ◽  
pp. 109
Author(s):  
N. Subramanian

In this paper, we define the sequence spaces: $\chi^{2qu}_{f\mu}\left(\Delta\right)$ and $\Lambda^{2qu}_{f\mu}\left(\Delta\right),$ where for any sequence $x=\left(x_{mn}\right),$ the difference sequence $\Delta x$ is given by $\left(\Delta x_{mn}\right)_{m,n=1}^{\infty}=\left[\left(x_{mn}-x_{mn+1}\right)-\left(x_{m+1n}-x_{m+1n+1}\right)\right]_{m,n=1}^{\infty}.$ We also study some properties and theorems of these spaces.


2012 ◽  
Vol 24 (7) ◽  
pp. 1882-1905 ◽  
Author(s):  
Sohan Seth ◽  
José C. Príncipe

Estimating conditional dependence between two random variables given the knowledge of a third random variable is essential in neuroscientific applications to understand the causal architecture of a distributed network. However, existing methods of assessing conditional dependence, such as the conditional mutual information, are computationally expensive, involve free parameters, and are difficult to understand in the context of realizations. In this letter, we discuss a novel approach to this problem and develop a computationally simple and parameter-free estimator. The difference between the proposed approach and the existing ones is that the former expresses conditional dependence in terms of a finite set of realizations, whereas the latter use random variables, which are not available in practice. We call this approach conditional association, since it is based on a generalization of the concept of association to arbitrary metric spaces. We also discuss a novel and computationally efficient approach of generating surrogate data for evaluating the significance of the acquired association value.


2014 ◽  
Vol 981 ◽  
pp. 279-286
Author(s):  
Fei Zhao ◽  
Si Zong Guo

For the objective fact that elements with different membership degrees should have different contribution to the metric measure between fuzzy numbers, this paper presents Lp-type of fuzzy number metrics weighted by structured element. Firstly, we define a metric weighted by structured element on the family (B[-1,1]) of all the same monotone and standard bounded functions on closed interval [-1,1] , and discuss the completeness and separability of those metric spaces; Next, using the fuzzy functional induced by normal fuzzy structured element, we give out a method that the metric of the closed bounded fuzzy number space is induced by the metric on function space B[-1,1]. Furthermore, a fuzzy number metric weighted by structured element which is induced by is presented ,and analyze completeness and separability of the induced fuzzy number metric spaces; Lastly, the difference and relationship between and the metric defined by traditional method are shown.


Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Wen Qing Fu ◽  
Sheng Gang Li ◽  
Harish Garg ◽  
Heng Liu ◽  
Ahmed Mostafa Khalil ◽  
...  

Metrics and their weaker forms are used to measure the difference between two data (or other things). There are many metrics that are available but not desired by a practitioner. This paper recommends in a plausible reasoning manner an easy-to-understand method to construct desired distance-like measures: to fuse easy-to-obtain (or easy to be coined by practitioners) pseudo-semi-metrics, pseudo-metrics, or metrics by making full use of well-known t-norms, t-conorms, aggregation operators, and similar operators (easy to be coined by practitioners). The simple reason to do this is that data for a real world problem are sometimes from multiagents. A distance-like notion, called weak interval-valued pseudo-metrics (briefly, WIVP-metrics), is defined by using known notions of pseudo-semi-metrics, pseudo-metrics, and metrics; this notion is topologically good and shows precision, flexibility, and compatibility than single pseudo-semi-metrics, pseudo-metrics, or metrics. Propositions and detailed examples are given to illustrate how to fabricate (including using what “material”) an expected or demanded WIVP-metric (even interval-valued metric) in practical problems, and WIVP-metric and its special cases are characterized by using axioms. Moreover, some WIVP-metrics pertinent to quantitative logic theory or interval-valued fuzzy graphs are constructed, and fixed point theorems and common fixed point theorems in weak interval-valued metric spaces are also presented. Topics and strategies for further study are also put forward concretely and clearly.


1962 ◽  
Vol 14 ◽  
pp. 149-155 ◽  
Author(s):  
E. L. Ruskol

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.


1997 ◽  
Vol 161 ◽  
pp. 491-504 ◽  
Author(s):  
Frances Westall

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.


1994 ◽  
Vol 144 ◽  
pp. 421-426
Author(s):  
N. F. Tyagun

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.


Author(s):  
Jules S. Jaffe ◽  
Robert M. Glaeser

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.


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