Determination of the Lower and Upper Bounds for Savings Circulating in National Economy and Impact of these Bounds on the Economy's Growth or Drop

1997 ◽  
Author(s):  
Alexei I. Krouglov
Keyword(s):  
National Economy ◽  
Upper Bounds ◽  
Lower And Upper Bounds

USE OF INTERPOLATION THEORY IN THE ANALYSIS OF GAS ADSORPTION ISOTHERMS: I. THEORY

1955 ◽  
Vol 33 (2) ◽  
pp. 193-202 ◽  
Author(s):  
J. M. Honig ◽  
P. C. Rosenbloom
Keyword(s):  
Adsorption Isotherms ◽  
Adsorption Process ◽  
Gas Adsorption ◽  
Upper Bounds ◽  
Interpolation Theory ◽  
Lower And Upper Bounds ◽  
Physical Quantities ◽  
Adsorbent System ◽  
Quantities Of Interest

The theory presented in this paper permits the determination of extremal bounds for a given adsorbate–adsorbent system within which the adsorption isotherms must fall if certain assumptions pertaining to the nature of the adsorption process are applicable. The use of interpolation theory in estimating lower and upper bounds on physical quantities of interest in adsorption theory is also discussed.

scholarly journals Assessment of Relevant Physical Phenomena Controlling Thermal Performance of Nanofluids

2006 ◽  
Author(s):  
M. Bahrami ◽  
M. M. Yovanovich ◽  
J. R. Culham
Keyword(s):  
Experimental Data ◽  
Systematic Approach ◽  
Large Degree ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Theoretical Studies ◽  
Lower And Upper Bounds ◽  
Physical Phenomena ◽  
Experimental And Theoretical Studies

This paper provides an overview of the important physical phenomena necessary for the determination of effective thermal conductivity of nanofluids. Through an investigation, a large degree of randomness and scatter has been observed in the experimental data published in the open literature. Given the inconsistency in the data, it is impossible to develop a comprehensive physical-based model that can predict all the trends. This also points out the need for a systematic approach in both experimental and theoretical studies. Upper and lower bounds are developed for steady-state conduction in stationary nanofluids. Comparisons between these bounds and the experimental data indicate that all the data (except for carbon nanotube data) lie between the lower and upper bounds.

scholarly journals Determination of lower and upper bounds of predicted production from history-matched models

2016 ◽  
Vol 20 (5) ◽  
pp. 1061-1073 ◽  
Author(s):  
G. M. van Essen ◽  
S. Kahrobaei ◽  
H. van Oeveren ◽  
P. M. J. Van den Hof ◽  
J. D. Jansen
Keyword(s):  
Upper Bounds ◽  
Lower And Upper Bounds

scholarly journals Some sharp circular and hyperbolic bounds of exp(-x2) with applications

2020 ◽  
Vol 14 (1) ◽  
pp. 239-254
Author(s):  
Yogesh Bagul ◽  
Christophe Chesneau
Keyword(s):  
Probability Theory ◽  
Simple Proof ◽  
Type A ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Sharp Bounds ◽  
Error Functions ◽  
Hyperbolic Cosine ◽  
Truncated Gaussian

This article is devoted to the determination of sharp lower and upper bounds for exp(-x2) over the interval (-?,?). The bounds are of the type [a+f(x)/a+1]? , where f(x) denotes either cosine or hyperbolic cosine. The results are then used to obtain and refine some known Cusa-Huygens type inequalities. In particular, a new simple proof of Cusa-Huygens type inequalities is presented as an application. For other interesting applications of the main results, sharp bounds of the truncated Gaussian sine integral and error functions are established. They can be useful in probability theory.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

scholarly journals Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 940
Author(s):  
Zijing Wang ◽  
Mihai-Alin Badiu ◽  
Justin P. Coon
Keyword(s):  
Value Of Information ◽  
Markov Models ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Lower And Upper Bounds ◽  
Uhlenbeck Process ◽  
Source Data ◽  
Non Linear ◽  
Queue Model ◽  
Selection Of

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

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