scholarly journals Influence in product spaces

2016 ◽  
Vol 48 (A) ◽  
pp. 145-152 ◽  
Author(s):  
Geoffrey R. Grimmett ◽  
Svante Janson ◽  
James R. Norris
Keyword(s):  
Product Space ◽  
Probability Space ◽  
Product Spaces ◽  
Sharp Threshold ◽  
Significant Aspect ◽  
Probabilistic Combinatorics ◽  
General Product

AbstractThe theory of influence and sharp threshold is a key tool in probability and probabilistic combinatorics, with numerous applications. One significant aspect of the theory is directed at identifying the level of generality of the product probability space that accommodates the event under study. We derive the influence inequality for a completely general product space, by establishing a relationship to the Lebesgue cube studied by Bourgain, Kahn, Kalai, Katznelson and Linial (BKKKL) in 1992. This resolves one of the assertions of BKKKL. Our conclusion is valid also in the setting of the generalized influences of Keller.

scholarly journals Fuzzy Inner Product Space: Literature Review and a New Approach

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 765
Author(s):  
Lorena Popa ◽  
Lavinia Sida
Keyword(s):  
Literature Review ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Comprehensive Overview ◽  
New Approach ◽  
Inner Product Spaces ◽  
Product Function ◽  
Suitable Definition

The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies on fuzzy inner product spaces, it is necessary to make a comprehensive overview of the published papers on the aforementioned subject in order to facilitate subsequent research. Then we considered another approach to the notion of fuzzy inner product starting from P. Majundar and S.K. Samanta’s definition. In fact, we changed their definition and we proved some new properties of the fuzzy inner product function. We also proved that this fuzzy inner product generates a fuzzy norm of the type Nădăban-Dzitac. Finally, some challenges are given.

A Brownian Agent Model for Analyzing Changes in a Nation's Product Space Structure

2015 ◽  
Vol 11 (1) ◽  
pp. 52-71
Author(s):  
Bin Jiang ◽  
Chao Yang ◽  
Takashi Yamada ◽  
Takao Terano
Keyword(s):  
Product Space ◽  
Initial Distribution ◽  
Space Structure ◽  
Product Spaces ◽  
Qualitative And Quantitative Analysis ◽  
Agent Model ◽  
Self Organized ◽  
Cooperative Production ◽  
Labor Resources ◽  
Agent Migration

This paper proposes a Brownian agent model for simulating and analyzing changes in a nation's product space structure. A measurement of proximity has been employed to quantify a relationship between two products and proved to be useful in product space analysis. This study employs such proximity measurement, and estimates a continued structure transformation of a nation's product space through feedback between agent movements and network evolutions. Labor resources of an enterprise or a firm are regarded as Brownian agents; they move through different product spaces for higher economic rewards. The simulation results show that trade areas were self-organized through Brownian agent migration and cooperative production with a random initial distribution. Furthermore, we have verified the applicability and efficiency of the model in analyzing changes in Chinese product space structure with empirical data. Main contributions of this paper are: 1) it provides a bottom-up model for analyzing changes of a nation's product space structure; and 2) it also provides both qualitative and quantitative analysis methods for a nation's product space structure.

scholarly journals Statistical Parameters Based on Fuzzy Measures

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2015
Author(s):  
Fernando Reche ◽  
María Morales ◽  
Antonio Salmerón
Keyword(s):  
Product Space ◽  
Fuzzy Measure ◽  
Joint Analysis ◽  
Product Spaces ◽  
Statistical Parameters ◽  
Fuzzy Measures ◽  
Reference Set

In this paper, we study the problem of defining statistical parameters when the uncertainty is expressed using a fuzzy measure. We extend the concept of monotone expectation in order to define a monotone variance and monotone moments. We also study parameters that allow the joint analysis of two functions defined over the same reference set. Finally, we propose some parameters over product spaces, considering the case in which a function over the product space is available and also the case in which such function is obtained by combining those in the marginal spaces.

scholarly journals Construction of Fuzzy Measures over Product Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1605 ◽  
Author(s):  
Fernando Reche ◽  
María Morales ◽  
Antonio Salmerón
Keyword(s):  
Product Space ◽  
Fuzzy Measure ◽  
Product Measure ◽  
Product Spaces ◽  
Joint Function ◽  
Single Product ◽  
Fuzzy Measures ◽  
Statistical Indices ◽  
Product Measures ◽  
Definition Of

In this paper, we study the problem of constructing a fuzzy measure over a product space when fuzzy measures over the marginal spaces are available. We propose a definition of independence of fuzzy measures and introduce different ways of constructing product measures, analyzing their properties. We derive bounds for the measure on the product space and show that it is possible to construct a single product measure when the marginal measures are capacities of order 2. We also study the combination of real functions over the marginal spaces in order to produce a joint function over the product space, compatible with the concept of marginalization, paving the way for the definition of statistical indices based on fuzzy measures.

scholarly journals On Bessel and Grüss inequalities for orthonormal families in inner product spaces

2004 ◽  
Vol 69 (2) ◽  
pp. 327-340 ◽  
Author(s):  
S. S. Dragomir
Keyword(s):  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces

A new reverse of Bessel's inequality for orthornormal families in real or complex inner product space is obtained. Applications for some Grüss type results are also provided.

Rigidity of entire graphs in weighted product spaces with nonnegative Bakry–Émery–Ricci tensor

2017 ◽  
Vol 17 (1) ◽  
Author(s):  
Henrique F. de Lima ◽  
Arlandson M. S. Oliveira ◽  
Márcio S. Santos
Keyword(s):  
Smooth Function ◽  
Mean Curvature ◽  
Ricci Tensor ◽  
Product Space ◽  
Product Spaces ◽  
Weighted Mean ◽  
Weighted Mean Curvature ◽  
Entire Graphs

AbstractWe study the rigidity of entire graphs defined over the fiber of a weighted product space whose Bakry–Émery–Ricci tensor is nonnegative. Supposing that the weighted mean curvature is constant and assuming appropriated constraints on the norm of the gradient of the smooth function

scholarly journals Characterizations of inner product spaces by means of norm one points

2005 ◽  
Vol 97 (1) ◽  
pp. 104
Author(s):  
José Mendoza ◽  
Tijani Pakhrou
Keyword(s):  
Convex Hull ◽  
Unit Sphere ◽  
Product Space ◽  
Normed Linear Space ◽  
Inner Product ◽  
Chebyshev Center ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Point Subset ◽  
Real Normed Linear Space

Let $X$ be a a real normed linear space of dimension at least three, with unit sphere $S_X$. In this paper we prove that $X$ is an inner product space if and only if every three point subset of $S_X$ has a Chebyshev center in its convex hull. We also give other characterizations expressed in terms of centers of three point subsets of $S_X$ only. We use in these characterizations Chebyshev centers as well as Fermat centers and $p$-centers.

scholarly journals On Carlsson type orthogonality and characterization of inner product spaces

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 859-870 ◽  
Author(s):  
Eder Kikianty ◽  
Sever Dragomir
Keyword(s):  
Normed Space ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Isosceles Orthogonality ◽  
Inner Product Spaces ◽  
Pythagorean Orthogonality

In an inner product space, two vectors are orthogonal if their inner product is zero. In a normed space, numerous notions of orthogonality have been introduced via equivalent propositions to the usual orthogonality, e.g. orthogonal vectors satisfy the Pythagorean law. In 2010, Kikianty and Dragomir [9] introduced the p-HH-norms (1 ? p < ?) on the Cartesian square of a normed space. Some notions of orthogonality have been introduced by utilizing the 2-HH-norm [10]. These notions of orthogonality are closely related to the classical Pythagorean orthogonality and Isosceles orthogonality. In this paper, a Carlsson type orthogonality in terms of the 2-HH-norm is considered, which generalizes the previous definitions. The main properties of this orthogonality are studied and some useful consequences are obtained. These consequences include characterizations of inner product space.

A proof of Garfunkel inequality and of some related results in inner product spaces

2017 ◽  
Vol 26 (2) ◽  
pp. 153-162
Author(s):  
DAN S¸ TEFAN MARINESCU ◽  
MIHAI MONEA
Keyword(s):  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Geometric Inequality ◽  
Product Spaces ◽  
Inner Product Spaces

In this paper, we will present a inner product space proof of a geometric inequality proposed by J. Garfunkel in American Mathematical Monthly [Garfunkel, J., Problem 2505, American Mathematical Monthly, 81 (1974), No. 11] and consider some other similar results.

A Comparison of Methods for Constructing Probability Measures on Infinite Product Spaces

1987 ◽  
Vol 30 (3) ◽  
pp. 282-285 ◽  
Author(s):  
Charles W. Lamb
Keyword(s):  
Probability Measure ◽  
Conditional Probability ◽  
Product Space ◽  
Infinite Product ◽  
Probability Measures ◽  
Classical Theorem ◽  
Comparison Of Methods ◽  
Product Spaces ◽  
Probability Functions ◽  
Finite Dimensional

AbstractThe construction, from a consistent family of finite dimensional probability measures, of a probability measure on a product space when the marginal measures are perfect is shown to follow from a classical theorem due to Ionescu Tulcea and known results on the existence of regular conditional probability functions.

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