NONLINEAR INTEGRAL INEQUALITY IN n INDEPENDENT VARIABLES WITH RETARDATION

In this paper,a nonlinear integral inequality in n independent variables with retardation is established,the result obtained generalizes and improves some previous results.

DISCRETE PHENOMENA IN THE UNIQUENESS OF THE CAUCHY PROBLEM IN MULTIPLE INDEPENDENT VARIABLES

This paper deals with discerete phenomena in uniqueness in the Cauchy problemsum from i?j=0 to n （i?j/0）aijuxixj+sum from i=0 to n（i/0）biuxi+cu=0,x0>0, u（0,x1,…,xn）=ux0（0,x1,…,xn） =0We prove that the problem only has trivial solutions in the neighbourhood of the origin, if bo（0）-Z sum from i=1 to n（i/1）（2ai + 1）λi≠0,λi>0 being the square roots of the eigenvalues of the product of matrices(?2aoo/?xi?xi（0）(i?j=i,….?and （aif（0））ii?f….,and ai being the arbitrarily non-negative integers.

Diabetes Risk Factor and Its Relationship to Increasing Coronavirus (COVID-19) Mortality Rate in United States in 2019-2022: An Epidemiological Study

As an effort to understand the effect of diabetes on the increasing rate of COVID-19 infection, we embarked upon a detailed statistical analysis of various datasets that include COVID-19 infection and mortality rate, diabetes and diseases that may contribute to the severity and risk factor of diabetes in individuals and this impact on COVID-19 and the mortality rate. These diseases include respiratory diseases, cardiovascular diseases, and obesity. Equally significant is the statistical analysis on ethnicity, age, and sex on COVID-19 infection as well as mortality rate. Their possible contributions to increasing the severity and risk factor of diabetes as a risk to mortality to individuals who have COVID-19. Objectives: The ultimate objectives of this investigation are as follow: 1) Is there a risk factor of diabetes on COVID-19 infection and increasing mortality rate? 2) To what extent do other disease conditions that include, obesity, heart failure, and respiratory diseases influence the severity and risk factor of diabetes on increasing COVID-19 infection and mortality rate? 3) To what extent does age, race, and gender increase the mortality of COVID-19 and increase the severity and risk factor of diabetes on COVID-19 mortality rate? 4) How and why COVID-19 virus increases the risk of diabetes in children? 5) Diabetes and COVID-19: Who is most at Risk? Lastly, understanding the misconception of COVID-19 and diabetes.

NOTES ON ERDOS' CONJECTURE

Let Xn,n ≥ 1, be a sequence of independent random variables satisfying P(Xn = 0) = 1 - P(Xn = an) = 1 - 1/Pn, where an,n ≥ 1, is a sequence of real numbers, and Pn is the nth prime,set FN(x) = P (N Xn ≤ x). The authors investigate a conjecture of Erdos in probabilistic number theory and show that in order for the sequence FN to be weakly convergent, it is both sufficient and necessary that there exist three numbers X0 and X1 < X2 such that limsup(FN(X2) - FN(X1)) > 0 holds, and Lo = N→ ∞ lim FN(X0) exists. Moreover, the authors point out that they can also obtain the same result in the weakened case of lim inf P(Xn = 0) > 0.

Extended Rama Distribution:Properties and Applications

In this paper,the Rama distribution(RD)is considered,and a new model called extended Rama distribution(ERD)is suggested.The new model involves the sum of two independent Rama distributed random variables.The probability density function(pdf)and cumulative distribution function(cdf)are obtained and analyzed.It is found that the new model is skewed to the right.Several mathematical and statistical properties are derived and proved.The properties studied include moments,coefficient of variation,coefficient of skewness,coefficient of kurtosis and moment generating function.Some simulations are undertaken to illustrate the behavior of these properties.In addition,the reliability analysis of the distribution is investigated through the hazard rate function,reversed hazard rate function and odds function.The parameter of the distribution is estimated based on the maximum likelihood method.The distributions of order statistics for ERD are also presented.The performance of the suggested model is compared with several other lifetime distributions based on some goodness of fit tests on a real dataset.It turns out that the suggested model is more flexible than its competitors considered in this study,for modeling real lifetime data.

Sharp large deviations for sums of bounded from above random variables

We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cram′er(1938), Bahadur and Ranga Rao(1960), and Sakhanenko(1991). In particular, our results extend Talagrand's inequality from bounded random variables to random variables having finite(2 + δ)-th moments, where δ∈(0, 1]. As a consequence,we obtain an improvement of Hoeffding's inequality. Applications to linear regression, self-normalized large deviations and t-statistic are also discussed.

On the asymptotic independence of the sum and maximum of normal random variables

RECENTLY, a number of papers have been published concerning the asymptotic independentproperties of V Xi and sum from 1 Xi of weakly dependent stationary sequence {Xi}.In this letter, let {Xi} be a standard normal sequence of random variables with zero meanand unit variance and write rij=cov（Xi, Xj）.