• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1229-1243
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• 2011

In this paper we consider a system of N-Laplacian elliptic equations with critical exponential growth. The existence and multiplicity results of solutions are obtained by a limit index method and Trudinger-Moser inequality.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.277-288
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• 2010

We consider the nonlinear biharmonic equation with coefficient exponential growth term and Dirichlet boundary condition. We show that the nonlinear equation has at least one bounded solution under the suitable conditions. We obtain this result by the variational method, generalized mountain pass theorem and the critical point theory of the associated functional.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.103-112
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• 2009

We show the existence of the solutions for the following nonlinear elliptic problem under the Dirichlet boundary condition. To show the existence of the solutions we use the variational formulation.

• The Journal of Information Technology
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• v.10 no.2
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• pp.47-64
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• 2007

Finite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. Accurate predictions of software release times, and estimation of the reliability and availability of a software product require quantification of a critical element of the software testing process : test coverage. This model called enhanced non-homogeneous poission process(ENHPP). In this paper, exponential coverage and S-coverage model was reviewed, proposes the exponentiated exponential coverage reliability model, which maked out efficiency substituted for gamma and Weibull model(2 parameter shape illustrated by Gupta and Kundu(2001). In this analysis of software failure data, algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on SSE statistics for the sake of efficient model, was employed.

• Journal of Information Science Theory and Practice
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• v.3 no.3
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• pp.75-80
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• 2015

Methods and Material: The PubMed database was used for retrieving data on 'cancer biology.' Articles were downloaded from the years 2000 to 2011. The articles were classified chronologically and transferred to a spreadsheet application for analysis of the data as per the objectives of the study. Statistical Method: To investigate the nature of growth of articles via exponential, linear, and logistics tests. Result: The year wise analysis of the growth of articles output shows that for the years 2000 to 2005 and later there is a sudden increase in output, during the years 2006 to 2007 and 2008 to 2011. The high productivity of articles during these years may be due to their significance in cancer biology literature, having received prominence in research. Conclusion: There is an obvious need for better compilations of statistics on numbers of publications in the years from 2000 to 2011 on various disciplines on a worldwide scale, for informed critical assessments of the amount of new knowledge contributed by these publications, and for enhancements and refinements of present Scientometric techniques (citation and publication counts), so that valid measures of knowledge growth may be obtained. Only then will Scientometrics be able to provide accurate, useful descriptions and predictions of knowledge growth.

• The Journal of Asian Finance, Economics and Business
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• v.9 no.1
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• pp.203-211
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• 2022

Foreign direct investment (FDI) has increased at an exponential rate during the last two decades. It is now a feature of emerging market economies as well. Foreign direct investment and financial development are important factors in an economy's growth. Various studies have examined the impact of foreign direct investment and financial development on economic growth in different countries and areas. However, the findings are currently inconclusive. Using updated data from 1970 to 2020, this study will examine the relationships between FDI, financial development, and economic growth in 30 rising economies.GDP is the dependent variable, while FDI, financial development, trade openness, infrastructure, exchange rate, and GDP growth are the independent factors. To estimate the panel data, we used the most recent econometric models. The study's major findings suggest that FDI and financial development are critical determinants in emerging economies' economic progress. Furthermore, multiple robustness checks supported the study's empirical findings. The results of this study include various practical recommendations for investors, governments, and policymakers, given the increased interest in global economic integration and member states' reliance on FDI as a critical aspect of sustaining prosperity.

• Biotechnology and Bioprocess Engineering:BBE
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• v.7 no.6
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• pp.362-366
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• 2002

A mathematical model has been developed for describing the oxygen concentration during the exponential growth of microorganisms, in a static solid substrate bed supported on a tray fermentor. The model equations comprise of one partial differential equation for mass transfer and an ordinary differential equation of growth. After nondimensionlisation, analytical solution tn the model has been obtained by the method of Laplace transforms. An expression for critical thickness of bed is deduced from the model equation. The significance of the model in the design of tray fermentors is discussed. The validity of the discussion is verified by taking an illustration from the literature.

• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.797-836
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• 2024

We consider the following strongly damped wave equation on ℝ³ with memory u_tt - αΔu_t - βΔu + λu - ∫₀^∞ κ'(s)∆u(t - s)ds + f(x, u) + g(x, u_t) = h, where a quite general memory kernel and the nonlinearity f exhibit a critical growth. Existence, uniqueness and continuous dependence results are provided as well as the existence of regular global and exponential attractors of finite fractal dimension.

• Food Science and Biotechnology
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• v.15 no.5
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• pp.773-777
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• 2006

Growth of Bacillus cereus was assessed during the storage of seasoned soybean sprouts at 0,5, 10, and $15^{\circ}C$. No lag time in its growth curve was observed and thus the specific growth rate of B. cereus in the exponential growth phase was estimated for bootstrapped microbial count data. The distribution of the specific growth rate could be explained by the BetaGeneral distribution function, and temperature dependence was described by the Ratkowsky square root model. The temperature dependence of the growth could be successfully incorporated into the differential equation of microbial growth to predict the B. cereus count on the seasoned soybean sprouts under fluctuating temperature conditions. Safe shelf lives with different probabilities to reach $10^5\;CFU/g$ were presented at four different temperatures, considering the variation in initial contamination and specific growth rate by the Monte Carlo method and 2-step bootstrapping, respectively. Safe shelf lives defined as the time with a probability of less than 0.1% of reaching the critical limit, were 13.4, 5.2, 3.6, and 2.8 days at 0, 5, 10, and $15^{\circ}C$, respectively.

• Journal of the Korea Society of Computer and Information
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• v.12 no.4
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• pp.33-42
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• 2007

Accurate predictions of software release times, and estimation of the reliability and availability of a software product require quantification of a critical element of the software testing process : test coverage. This model called Enhanced non-homogeneous poission process(ENHPP). In this paper, exponential coverage and S-shaped model was reviewed, proposes the Kappa coverage model, which maked out efficiency application for software reliability. Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on SSE statistics and Kolmogorov distance, for the sake of efficient model, was employed. From the analysis of mission time, the result of this comparative study shows the excellent performance of Burr coverage model rather than exponential coverage and S-shaped model using NTDS data. This analysis of failure data compared with the Kappa coverage model and the existing model(using arithmetic and Laplace trend tests, bias tests) is presented.