Multiplicity Results for Second-order Generalized Sturm-Liouville Boundary Value Problems with Dependence on the First Order Derivative

By using fixed point theorems,we consider multiplicity of positive solutions for second-order generalized Sturm-Liouville boundary value problem,where the first order derivative is involved in the nonlinear term explicitly.We show the existence of multiple positive solutions for the problems.Example is given to illustrate the main results of the article.

Randomized Generalized Singular Value Decomposition

The generalized singular value decomposition(GSVD)of two matrices with the same number of columns is a very useful tool in many practical applications.However,the GSVD may suffer from heavy computational time and memory requirement when the scale of the matrices is quite large.In this paper,we use random projections to capture the most of the action of the matrices and propose randomized algorithms for computing a low-rank approximation of the GSVD.Serval error bounds of the approximation are also presented for the proposed randomized algorithms.Finally,some experimental results show that the proposed randomized algorithms can achieve a good accuracy with less computational cost and storage requirement.

Analyzing the Annual Maximum Magnitude of Earthquakes in Japan by Extreme Value Theory

One of the most important and interesting issues associated with the earthquakes is the long-term trend of the extreme events. Extreme value theory provides methods for analysis of the most extreme parts of data. We estimated the annual maximum magnitude of earthquakes in Japan by extreme value theory using earthquake data between 1900 and 2019. Generalized extreme value (GEV) distribution was applied to fit the extreme indices. The distribution was used to estimate the probability of extreme values in specified time periods. The various diagnostic plots for assessing the accuracy of the GEV model fitted to the magnitude of maximum earthquakes data in Japan gave the validity of the GEV model. The extreme value index, ξ was evaluated as −0.163, with a 95% confidence interval of [−0.260, −0.0174] by the use of profile likelihood. Hence, the annual maximum magnitude of earthquakes has a finite upper limit. We obtained the maximum return level for the return periods of 10, 20, 50, 100 and 500 years along with their respective 95% confidence interval. Further, to get a more accurate confidence interval, we estimated the profile log-likelihood. The return level estimate was obtained as 7.83, 8.60 and 8.99, with a 95% confidence interval of [7.67, 8.06], [8.32, 9.21] and [8.61, 10.0] for the 10-, 100- and 500-year return periods, respectively. Hence, the 2011 off the Pacific coast of Tohoku Earthquake, which was the largest in the observation history of Japan, had a magnitude of 9.0, and it was a phenomenon that occurs once every 500 year.

Red Tide Frequency Analysis Using the Extreme Value Theory

In recent years, the red tide erupted frequently, and caused a great economic loss. At present, most literatures emphasize the academic research on the growth mechanism of red tide alga. In order to find out the characters of red tide in detail and improve the precision of forecast, this paper gives some new approaches to dealing with the red tide. By the extreme values, we deal with the red tide frequency analysis and get the estimation of T-times red tide level U (T), which is the level once the consistence of red tide alga exceeds on the average in a period of T times.

Empirical Analysis of Value-at-Risk Estimation Methods Using Extreme Value Theory

This paper investigates methods of value-at-risk (VaR) estimation using extreme value theory (EVT). It compares two different estimation methods, 'two-step subsample bootstrap' based on moment estimation and maximum likelihood estimation (MLE), according to their theoretical bases and computation procedures. Then, the estimation results are analyzed together with those of normal method and empirical method. The empirical research of foreign exchange data shows that the EVT methods have good characters in estimating VaR under extreme conditions and 'two-step subsample bootstrap' method is preferable to MLE.

SOME INEQUALITIES OF GENERALIZED SINGULAR VALUES OF MATRICES

@1 Definition 1 Let A=(αij)∈Cn×n,B=(bij)∈Cn×n,is nonsingular.The generalizedsingular values of A（relative to B）are following determinate nonnegative real numberswhen ||·||2 denotes the Euclid vector norm,〈n〉={1,2,…,n}.Definition 2 Let A,B∈Cn×n,if there exist λ∈C and x∈Cn\{0}。

Applications of Bootstrap in Analyzing General Extreme Value Distributions

The bootstrap method is one of the new ways of studying statistical math which this article uses but is a major tool for studying and evaluating the values of parameters in probability distribution.Our research is concerned overview of the theory of infinite distribution functions.The tool to deal with the problems raised in the paper is the mathematical methods of random analysis(theory of random process and multivariate statistics).In this article,we introduce the new function to find out the bias and standard error with jackknife method for Generalized Extreme Value distributions.

The Necessary and Sufficient Conditions for Two Kinds of Matrix Equtions Having Semipositive Subdefinite Solutions

Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric positive definite or sysmmetric semiposite definite matrices respectively . Recently, however, attentions are been paying to the situation for S to be the set of general(semi) positive definite matrices(called as semipositive subdefinite matrices below) . In this paper the necessary and sufficient conditions for the following two kinds of matrix equations having semipositive, subdefinite solutions are obtained. General solutions and symmetric solutions of the equations (Ⅰ) and (Ⅱ) have been considered in in detail.

A Newly-Discovered GPD-GEV Relationship Together with Comparing Their Models of Extreme Precipitation in Summer

It has been theoretically proven that at a high threshold an approximate expression for a quantile of GEV （Generalized Extreme Values） distribution can be derived from GPD （Generalized Pareto Distribution）. Afterwards, a quantile of extreme rainfall events in a certain return period is found using L-moment estimation and extreme rainfall events simulated by GPD and GEV, with all aspects of their results compared. Numerical simulations show that POT （Peaks Over Threshold）-based GPD is advantageous in its simple operation and subjected to practically no effect of the sample size of the primitive series, producing steady high-precision fittings in the whole field of values （including the high-end heavy tailed）. In comparison, BM （Block Maximum）-based GEV is limited, to some extent, to the probability and quantile simulation, thereby showing that GPD is an extension of GEV, the former being of greater utility and higher significance to climate research compared to the latter.

Spatial Modeling of the Highest Daily Maximum Temperature in Korea via Max-stable Processes

This paper examines the annual highest daily maximum temperature （DMT） in Korea by using data from 56 weather stations and employing spatial extreme modeling. Our approach is based on max-stable processes （MSP） with Schlather＇s characterization. We divide the country into four regions for a better model fit and identify the best model for each region. We show that regional MSP modeling is more suitable than MSP modeling for the entire region and the pointwise generalized extreme value distribution approach. The advantage of spatial extreme modeling is that more precise and robust return levels and some indices of the highest temperatures can be obtained for observation stations and for locations with no observed data, and so help to determine the effects and assessment of vulnerability as well as to downscale extreme events.

Simulation of Precipitation in Monsoon Regions of China by CMIP3 Models

The output of 25 models used in the Coupled Model Intercomparison Project phase 3 (CMIP3) were evaluated,with a focus on summer precipitation in eastern China for the last 40 years of the 20th century.Most mod-els failed to reproduce rainfall associated with the East Asian summer monsoon (EASM),and hence the seasonal cycle in eastern China,but provided reasonable results in Southwest (SW) and Northeast China (NE).The simula-tions produced reasonable results for the Yangtze-Huai (YH) Basin area,although the Meiyu phenomenon was underestimated in general.One typical regional phe-nomenon,a seasonal northward shift in the rain belt from early to late summer,was completely missed by most models.The long-term climate trends in rainfall over eastern China were largely underestimated,and the ob-served geographical pattern of rainfall changes was not reproduced by most models.Precipitation extremes were evaluated via parameters of fitted GEV (Generalized Ex-treme Values) distributions.The annual extremes were grossly underestimated in the monsoon-dominated YH and SW regions,but reasonable values were calculated for the North China (NC) and NE regions.These results suggest a general failure to capture the dynamics of the EASM in current coupled climate models.Nonetheless,models with higher resolution tend to reproduce larger decadal trends and annual extremes of precipitation in the regions studied.

Hybrid NOMA Based MIMO Offloading for Mobile Edge Computing in 6G Networks

Non-orthogonal multiple access (NOMA), multiple-input multiple-output (MIMO) and mobile edge computing (MEC) are prominent technologies to meet high data rate demand in the sixth generation (6G) communication networks. In this paper, we aim to minimize the transmission delay in the MIMO-MEC in order to improve the spectral efficiency, energy efficiency, and data rate of MEC offloading. Dinkelbach transform and generalized singular value decomposition (GSVD) method are used to solve the delay minimization problem. Analytical results are provided to evaluate the performance of the proposed Hybrid-NOMA-MIMO-MEC system. Simulation results reveal that the H-NOMA-MIMO-MEC system can achieve better delay performance and lower energy consumption compared to OMA.

Local and regional flood frequency analysis based on hierarchical Bayesian model in Dongting Lake Basin,China

This study developed a hierarchical Bayesian(HB)model for local and regional flood frequency analysis in the Dongting Lake Basin,in China.The annual maximum daily flows from 15 streamflow-gauged sites in the study area were analyzed with the HB model.The generalized extreme value(GEV)distribution was selected as the extreme flood distribution,and the GEV distribution location and scale parameters were spatially modeled through a regression approach with the drainage area as a covariate.The Markov chain Monte Carlo(MCMC)method with Gibbs sampling was employed to calculate the posterior distribution in the HB model.The results showed that the proposed HB model provided satisfactory Bayesian credible intervals for flood quantiles,while the traditional delta method could not provide reliable uncertainty estimations for large flood quantiles,due to the fact that the lower confidence bounds tended to decrease as the return periods increased.Furthermore,the HB model for regional analysis allowed for a reduction in the value of some restrictive assumptions in the traditional index flood method,such as the homogeneity region assumption and the scale invariance assumption.The HB model can also provide an uncertainty band of flood quantile prediction at a poorly gauged or ungauged site,but the index flood method with L-moments does not demonstrate this uncertainty directly.Therefore,the HB model is an effective method of implementing the flexible local and regional frequency analysis scheme,and of quantifying the associated predictive uncertainty.

How Frequently Will the Persistent Heavy Rainfall over the Middle and Lower Yangtze River Basin in Summer 2020 Happen under Global Warming?

The middle and lower Yangtze River basin(MLYRB)suffered persistent heavy rainfall in summer 2020,with nearly continuous rainfall for about six consecutive weeks.How the likelihood of persistent heavy rainfall resembling that which occurred over the MLYRB in summer 2020(hereafter 2020PHR-like event)would change under global warming is investigated.An index that reflects maximum accumulated precipitation during a consecutive five-week period in summer(Rx35day)is introduced.This accumulated precipitation index in summer 2020 is 60%stronger than the climatology,and a statistical analysis further shows that the 2020 event is a 1-in-70-year event.The model projection results derived from the 50-member ensemble of CanESM2 and the multimodel ensemble(MME)of the CMIP5 and CMIP6 models show that the occurrence probability of the 2020PHR-like event will dramatically increase under global warming.Based on the Kolmogorov-Smirnoff test,one-third of the CMIP5 and CMIP6 models that have reasonable performance in reproducing the 2020PHR-like event in their historical simulations are selected for the future projection study.The CMIP5 and CMIP6 MME results show that the occurrence probability of the 2020PHR-like event under the present-day climate will be double under lower-emission scenarios(CMIP5 RCP4.5,CMIP6 SSP1-2.6,and SSP2-4.5)and 3-5 times greater under higher-emission scenarios(3.0 times for CMIP5 RCP8.5,2.9 times for CMIP6 SSP3-7.0,and 4.8 times for CMIP6 SSP5-8.5).The inter-model spread of the probability change is small,lending confidence to the projection results.The results provide a scientific reference for mitigation of and adaptation to future climate change.

CHARACTERISTICS OF SUBDIFFERENTIALS OF FUNCTIONS

In the presem paper, some important characteristics of Fenchel-, Frechet-,Hademard-, and Gateaux-Subdifferentials are showed up, and properties of functions, especially. convexity of functions, are described by subdifferentials.

Spatial Distribution of High-temperature Risk with a Return Period of Different Years in the Yangtze River Delta Urban Agglomeration

Against the background of global warming,research on the spatial distribution of high-temperature risk is of great significance to effectively prevent the adverse effects of high temperatures.By using air temperature data from 1951 to 2018 measured by meteorological stations located in the Yangtze River Delta urban agglomeration,the daily maximum air temperature distribution is interpolated at a resolution of 1 km based on the local thin disk smooth spline function;the high-temperature threshold for return periods of 5,10,20 and 30 yr are then calculated by using the generalized extreme value method.The yearly average high-temperature intensity and high-temperature days are finally calculated as high-temperature danger factors.Socioeconomic statistical data and remotely sensed image data in 2018 are used as the background data to calculate the spatial distribution of high-temperature vulnerability factors and prevention capacity factors,which are then used to compute the high-temperature risk index during different recurrence periods in the Yangtze River Delta urban agglomerations.The results show that the spatial distribution features of high-temperature risk in different return periods are similar.The high-temperature risk index gradually increases from northeast to southwest and from east coast to inland,which has obvious latitude variation characteristics and a relationship with the comprehensive influence of the underlying surface and urban scale.In terms of time variation,the high-temperature risk index and its spatial distribution difference gradually decreases with increasing return period.In different cities,the high-temperature risk in the central area of the city is generally higher than that in the surrounding suburban areas.Jinhua,Hangzhou of Zhejiang Province and Xuancheng of Anhui Province are the top three cities with high-temperature risk in the study area.

Confirmation of the Record of the Serpent Eel, Ophisurus serpens （Family： Ophichthidae） from Mersin Bay （NE Mediterranean, Turkey）

A specimen of the serpent eel, Ophisurus serpens, with a total length of 190.2 cm was caught off the coast of Mersin （Incekum）, Turkey on November 2014 during trawling. This manuscript presents the first digitized specimen of O. serpens from the Mersin Bay （northeastern Mediterranean）, and hence, confirms the presence of the species in the northeastern Mediterranean despite a suspicious previous report, possibly mistaken with Echelus myrus, of the species from Yumurtahk Bay. Remarks on the morphology and geographical distribution of the species in the Mediterranean Sea, Turkey are given.

A Note on a Problem of M. S. Berger

In this paper, we discuss the problem concerning global and local structure of solutions of an operator equation posed by M. S. Berger. Let f : U (?)E→ F be a C1 map, where E and F are Banach spaces and U is open in E. We show that the solution set of the equation f(x)=y for a fixed generalized regular value y of f is represented as a union of disjoint connected C1 Banach submanifolds of U, each of which has a dimension and its tangent space is given. In particular, a characterization of the isolated solutions of the equation f(x) = y is obtained.

Assesment of Frequency-Magnitude of Extreme Rainfall Events-Case Study of the MeKong River Delta

Extreme rainfall events are primary natural hazards, which cause a severe threat to people and their properties in populated cities, which are normally located in coastal areas in Vietnam. Analysing these events by using a data series observed over years will support us to draw a picture of how the climate change impact on local environments. The purpose of this report is to understand the characteristics of the extreme rainfall events in MEKONG river delta （south VietNam）. Daily rainfall data in the period of 30 years for a meteorological station in each area were collected from the Vietnam National Hydro-meteorological Service. The extreme rainfall events were defined as those exceeding the 95th percentile for each station. The analytical results show that the rainfall values （95th percentile） are 37.4 mm/day at Nam Can station, 27 mm/day at My Thanh station, 22.4 mm/day at Hoa Binh station, 23.8 mm/day at Binh Dai station and 22.7 mm/day at Ben Trai station. The highest rainfall data ever recorded are 246.4 mm/day （Nam Can）, 174.5 mm/day （My Thanh）, 179 mm/day （Hoa Bin_h）, 187.3 mm/day （Binh Dai） and 136.3 mm/day （Ben Trai） during 1983-2012. The result of the Mann-Kendall tests show that there was a significant creasing of the rainfall at Nam Can, My Thanh station in two periods （1983-2012, 1998-2012） while no clear trend of the rainfall was recoreded at Hoa Birth, Binh Dai, Ben Trai station. In order to estimate the return period of the extreme rainfall events, the method General Extreme Value Distribution was used to calculate frequent distribution. The magnitudes of daily maximum rainfall were from 2 to 100 years. The results of return period show that maximum rainfalls are 46.6 mm at Nam Can station （highest） and 31.4 mm at Hoa Birth station （lowest） during 50 years. Similarly, maximum rainfalls are expected to be about 55.1 mm at Nam Can station and 37.2 mm at Hoa Birth station for 100 years.

Parametric and Non-Parametric Survival Analysis of Patients with Acute Myeloid Leukemia (AML)

Background: Acute Myeloid leukemia (AML) is the most prominent acute leukemia in adults. In the United States, we experience over 20,000 cases per year. Over the past decade, improvements in the diagnosis of subtypes of AML and advances in therapeutic approaches have improved the outlook for patients with AML. However, despite these advancements, the survival rate among patients who are less than 65 years of age is only 40 percent. Purpose: The purpose of the paper is to study if there exists any significant difference in the survival probabilities of male and female AML patients. Also, we want to investigate if there is any parametric probability distribution that best fits the male and female patient survival and compare the survival probabilities with the non-parametric Kaplan-Meier (KM) method. Methods: We used both parametric and non-parametric statistical methods to perform the survival analysis to assess the survival probabilities of 2015 patients diagnosed with AML. Results: We found evidence of a statistically significant difference between the mean survival time of male and female patients diagnosed with AML. We performed parametric survival analysis and found a Generalized Extreme Value (GEV) distribution best fitting the data of the survival time for male and female patients. We then estimated the survival probabilities and compared them with the frequently used non-parametric Kaplan-Meier (KM) survival method. Conclusion: The comparison between the survival probability estimates of the two methods revealed a better survival probability estimate by the parametric method than the Kaplan-Meier. We also compared the median survival time of male and female patients individually with descriptive, parametric, and non-parametric methods of analysis. The parametric survival analysis is more robust and efficient because it is based on a well-defined parametric probabilistic distribution, hence preferred over the non-parametric Kaplan-Meier estimate. This study offers therapeutic significance for further enhancement to treat patients with Acute Myeloid Leukemia.