Estimation of Return Level for Maximum Daily and Hourly Precipitation in Nagano Prefecture, Japan, Using the Extreme Value Theory

The weather in Nagano Prefecture, Japan, can be roughly classified into four types according to principal component analysis and k-means clustering. We predicted the extreme values of the maximum daily and hourly precipitation in Nagano Prefecture using the extreme value theory. For the maximum daily precipitation, the vales of ξ in Matsumoto, Karuizawa, Sugadaira, and Saku were positive;therefore, it has no upper bound and tends to take large values. Therefore, it is dangerous and caution is required. The values of ξ in Nagano, Kisofukushima, and Minamishinano were determined to be zero, therefore, there was no upper limit, the probability of obtaining a large value was low, and caution was required. We predicted the maximum return levels for return periods of 10, 20, 50, and 100 years along with respective 95% confidence intervals in Nagano, Matsumoto, Karuizawa, Sugadaira, Saku, Kisofukushima, and Minamishinano. In Matsumoto, the 100-year return level was 182 mm, with a 95% CI [129, 236]. In Minamishinano, the 100-year return level was 285 mm, with a 95% CI [173, 398]. The 100-year return levels for the maximum daily rainfall were 285, 271, and 271 mm in Minamishinano, Saku, and Karuizawa, respectively, where the changes in the daily maximum rainfall were larger than those at other points. Because these values are large, caution is required during heavy rainfall. The 100-year return levels for the maximum daily and hourly precipitation were similar in Karuizawa and Saku. In Sugadaira, the 100-year return level for a maximum hourly rainfall of 107.2 mm was larger than the maximum daily rainfall. Hence, it is necessary to be careful about short-term rainfall events.

On the Mean Value of High-Powers of a Special Character Sum Modulo a Prime

In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,and derive an exact computational formula.It can be conveniently programmed by the“Mathematica”software,by which we can get the exact results easily.

THE SCHUR CONVEXITY OF GINI MEAN VALUES IN THE SENSE OF HARMONIC MEAN

We prove that the Gini mean values S（a,b; x,y） are Schur harmonic convex with respect to （x,y）∈（0,∞）×（0,∞） if and only if （a, b） ∈{（a, b）：a≥0,a ≥ b,a＋b＋1≥0}∪{（a,b）：b≥0,b≥a,a＋b＋1≥0} and Schur harmonic concave with respect to （x,y） ∈ （0,∞）×（0,∞） if and only if （a,b）∈{（a,b）：a≤0,b≤0,a｜b｜1≤0}.

The Asymptotic Property of Generalized Taylor Remainder "Mean Value Point"

This paper discussed asymptotic property of Taylor remainder 'mean value point' in normed Linear space. The asymptotic progerty of 'mean value point' is solved when f(n+i)(x0)h(n+i) = 0(i = 1, 2,..., p - 1) and f(n+p)(x0)h(h+p) don't exist. Meanwhile, achieve more general asymptotic estimation formula. Make many former results are just because of special case of the pager.

Some Hybrid Mean Values of a New Number Theoretic Function

Let p and q be two distinct primes, epq（n） denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq（n）, and give some hybrid mean value formulas for epq（n） and Dirichlet divisor function d（n）. Key words： largest exponent; asymptotic formula; hybrid mean value; Dirichlet divisor function d（n）

THE MEAN VALUE THEOREM AND CONVERSE THEOREM OF ONE CLASS THE FOURTH-ORDER PARTIAL DIFFERENTIAL EQUATIONS

For the formal presentation about the definite problems of ultra-hyperbolic equations, the famous Asgeirsson mean value theorem has answered that Cauchy problems are ill-posed to ultra-hyperbolic partial differential equations of the second-order. So it is important to develop Asgeirsson mean value theorem. The mean value of solution for the higher order equation hay been discussed primarily and has no exact result at present. The mean value theorem for the higher order equation can be deduced and satisfied generalized biaxial symmetry potential equation by using the result of Asgeirsson mean value theorem and the properties of derivation and integration. Moreover, the mean value formula can be obtained by using the regular solutions of potential equation and the special properties of Jacobi polynomials. Its converse theorem is also proved. The obtained results make it possible to discuss on continuation of the solutions and well posed problem.

Hybrid Mean Value of the Hyper Cochrane Sums

The main purpose of this paper is to use the analytic methods to study the hybrid mean value involving the hyper Cochrane sums, and give several sharp asymptotic formulae.

Mean Values of the Hardy Sum

Let p≥5 be a prime. For any integer h, the Hardy sum is defined by H(h,p)=sum((-1)^(j+1+[(hj)/p]))from (p-1) to (j=1) which is related to the classical Dedekind sum. The mean values of the Hardy sum in short intervals are studied by using the mean value theorems of Dirichlet L-functions.

On the Mean Value of the Infinite Order Legendre Series

In this paper, we studies the relations between the mean value and the maximun norm of the infinite order entire functions which defined by legendre series. We obtained that if f(z) is an infinite order entire function with a positive exponenatial lower order. then loaM (α) ～logMδ(α) ～ logMδ(α) (α→+∞).

On the Lucas Base and Computation of Counting Function Mean Value

In this paper, we introduce a new counting function a(m) related to the Lucas number, then use conjecture and induction methods to give an exact formula Ar(N)=α(n), (r=1,2,3) and prove them.

Three Versions on tian's Translations in Doctrine of the Mean

Since ancient times,"heaven"has been indispensable in the traditional books of the communist party of China.The English translation of traditional books has become the mainstream of The Times.Currently,the translation levels of the translated versions are uneven,and there are great differences in the translation of some keywords.This paper mainly discusses the different translations of"heaven"in section 1 of the English translation of theof the Mean by James Legge,Gu Hongming,Roger T.Ames and David Hall.

THE DYADIC DERIVATIVE AND CESRO MEAN OF BANACH-VALUED MARTINGALES

In this article, the Banach space X and the martingales with values in it are considered. It is shown that the maximal operators of the one-dimensional dyadic derivative of the dyadic integral and Cesaro means are bounded from the dyadic Hardy- Lorentz space pH^-ra（X） to Lra（X） when X is isomorphic to a p-uniformly smooth space （1 〈p ≤ 2）. And it is also bounded from Hra（X） to Lra（X） （0 〈 r 〈 ∞,0 〈 a≤oc） when X has Radon-Nikodym property. In addition, some weak-type inequalities are given.

Effect of Sea Level Variation on Tidal Characteristic Values for the East China Sea

Tidal waves in the East China Sea are simulated numerically with POM(Princeton Ocean Model) model for normal mean sea level, 30 cm higher, 60 cm higher, and 100 cm higher, respectively, and the simulated result is compared with the harmonic analysis result of hourly sea level data from 19 tide gauges for more than 19 years. It is indicated that the long-term mean sea level variation affects notably tidal waves in this region. Generally, the tidal amplitude increases when the mean sea level rises, but this relationship may be inverse for some sea areas. The maximal variation of tidal amplitude takes place in the zones near the Fujian coast and the Zhejiang coast, rather than the shallowest Bohai Sea. The maximum increase of M2 amplitude can exceed about 15 cm corresponding to the 60 cm rise of the mean sea level along the Fujian coast. The other regions with large variations of tidal amplitude are those along the Jiangsu coast, the south-east coast of Shandong, and the south-east coast of Dalian. The propagation of tidal waves is also related to mean sea level variation, and the tidal phase-lag decreases generally when the mean sea level rises. Almost all the regions where the tidal phase-lag increases with rising mean sea level are close to amphidromic points, meanwhile the spatial area of such regions is very small. Because the influence of mean sea level variation upon tidal waves is spatially marked, such spatial effect should be considered in calculation of the tidal characteristic value and engineering water level. In the region where the amplitudes of the major tidal constituents increase, the probable maximum high water level becomes higher, the probable maximum low water level becomes lower, and both design water level andcheck water level increase obviously. For example, the design water level at Xiamen increases by 13.5 cm due to the variation of tidal waves when the mean sea level rises 60 cm, the total increase of design water level being 73.5 cm.

Meridional Distributions of Historical Zonal Averages and Their Use to Quantify the Global and Spheroidal Mean Near-Surface Temperature of the Terrestrial Atmosphere

The zonal averages of temperature (the so-called normal temperatures) for numerous parallels of latitude published between 1852 and 1913 by Dove, Forbes, Ferrel, Spitaler, Batchelder, Arrhenius, von Bezold, Hopfner, von Hann, and Börnstein were used to quantify the global (spherical) and spheroidal mean near-surface temperature of the terrestrial atmosphere. Only the datasets of Dove and Forbes published in the 1850s provided global averages below 〈T〉=14°C, mainly due to the poor coverage of the Southern Hemisphere by observations during that time. The global averages derived from the distributions of normal temperatures published between 1877 and 1913 ranged from 〈T〉=14.0°C (Batchelder) to 〈T〉=15.1°C (Ferrel). The differences between the global and the spheroidal mean near-surface air temperature are marginal. To examine the uncertainty due to interannual variability and different years considered in the historic zonal mean temperature distributions, the historical normal temperatures were perturbed within ±2σ to obtain ensembles of 50 realizations for each dataset. Numerical integrations of the perturbed distributions indicate uncertainties in the global averages in the range of ±0.3°C to ±0.6°C and depended on the number of available normal temperatures. Compared to our results, the global mean temperature of 〈T〉=15.0°C published by von Hann in 1897 and von Bezold in 1901 and 1906 is notably too high, while 〈T〉=14.4°C published by von Hann in 1908 seems to be more adequate within the range of uncertainty. The HadCRUT4 record provided 〈T〉≌?13.7°C for 1851-1880 and 〈T〉=13.6°C for 1881-1910. The Berkeley record provided 〈T〉=13.6°C and 〈T〉≌?13.5°C for these periods, respectively. The NASA GISS record yielded 〈T〉=13.6°C for 1881-1910 as well. These results are notably lower than those based on the historic zonal means. For 1991-2018, the HadCRUT4, Berkeley, and NASA GISS records provided 〈T〉=14.4°C, 〈T〉=14.5°C, and 〈T〉=14.5°C, respectively. The comparison of the 1991-2018 globally averaged near-surface temperature with those derived from distributions of zonal temperature averages for numerous parallels of latitude suggests no change for the past 100 years.

The Expected Value of a Fuzzy Number

Conjunction of two probability laws can give rise to a possibility law. Using two probability densities over two disjoint ranges, we can define the fuzzy mean of a fuzzy variable with the help of means two random variables in two disjoint spaces.

Two Modifications of Weight Calculation of the Non-Local Means Denoising Method

The non-local means (NLM) denoising method replaces each pixel by the weighted average of pixels with the sur-rounding neighborhoods. In this paper we employ a cosine weighting function instead of the original exponential func-tion to improve the efficiency of the NLM denoising method. The cosine function outperforms in the high level noise more than low level noise. To increase the performance more in the low level noise we calculate the neighborhood si-milarity weights in a lower-dimensional subspace using singular value decomposition (SVD). Experimental compari-sons between the proposed modifications against the original NLM algorithm demonstrate its superior denoising per-formance in terms of peak signal to noise ratio (PSNR) and histogram, using various test images corrupted by additive white Gaussian noise (AWGN).

A Number Theoretic Function and Its Mean Value Computation

Let p be a prime, n be any positiv e integer, α(n,p) denotes the power of p in the factorization of n! . In this paper, we give an exact computing formula of the mean value ∑ n<Nα(n,p).

The Ethics and the Meaning of Life among College Students

The concern of the ethics and the meaning of life in young adults became universal and are present in all contexts of human life. Such universality is due to the development of modern rationality, to establish a relationship between the intrinsic theoretical dimensions (scientific) and practical dimensions (ethical), originated that are present in the own array of knowledge. This descriptive cross-sectional study, aims to identify the values of the ethical dimension and meaning of life defended by the college students of the Universities of Madeira, Portugal and Fortaleza, Brazil. The sample consists of 605 University students (Madeira = 225 and Fortaleza = 380), with an average age of 21 years and a standard deviation of 2. We used the questionnaire on values (adapted from the European Values Survey). Most of the young people referred to have a religion (60% wood and 78.4% stronghold), being the most Catholic, however, present in your frequency disinterest and, yet, in Brazil there is a greater diversity of religions. Supporting the intervention of religious institutions in situations of everyday life is accepted mostly by Brazilians, with the exception of politics (35.5%). On the other hand, the university students of the University of Madeira understand that Religious Institutions should only give their opinion on racial discrimination (76.6%). Believe in God (90.8% and 55.1% Stronghold) and Soul (80.3% and 66.4% Stronghold) are beliefs more referred to by college students. These results are intended to contribute in the field of research on ethical values and meaning of life in young people. This study contributes to future comparative research among university students and to developing strategic programs in education and health, increasing the success and excellence in the formation of a full citizenship, preventing the fanaticisms and the social discrimination that today devastate the collective globally.

Some Mean Convergence Theorems for the Maximum of Normed Double Sums of Banach Space Valued Random Elements

In this correspondence,we establish mean convergence theorems for the maximum of normed double sums of Banach space valued random elements.Most of the results pertain to random elements which are M-dependent.We expand and improve a number of particular cases in the literature on mean convergence of random elements in Banach spaces.One of the main contributions of the paper is to simplify and improve a recent result of Li,Presnell,and Rosalsky[Journal of Mathematical Inequalities,16,117–126(2022)].A new maximal inequality for double sums of M-dependent random elements is proved which may be of independent interest.The sharpness of the results is illustrated by four examples.

Stability of gyrotheodolite

The checking methods of gyrotheodolite stability were proposed. The main factors estimating the stability of gyrotheodolite were determined. They are the stability of the mean value of oscillating, zero position and the quality of magnet shield. The evaluation mathematical model for gyrotheodolite stability was established based upon the principle of fuzzy mathematics and an effective method of quantitative analysis of the gyrotheodolite stability was presented. By taking JT15 and other gyrotheodolites for examples, the effect of voltage and frequency on the rotational speed of gyro-motor and on the stability of the mean value of oscillating of gyro, the influence of temperature, magnetic field, vibration on stability of gyrotheodolite was studied. At last some concrete measurements for enhancing the stability of orientating precision of the gyro were suggested.