NORMAL FAMILIES AND SHARED VALUES OF HOLOMORPHIC FUNCTIONS

Let F be a family of holomorphic functions in a domain D, k be a positive integer, a, b（≠0）, c（≠0） and d be finite complex numbers. If, for each f∈F, all zeros of f-d have multiplicity at least k, f^（k） = a whenever f=0, and f=c whenever f^（k） = b, then F is normal in D. This result extends the well-known normality criterion of Miranda and improves some results due to Chen-Fang, Pang and Xu. Some examples are provided to show that our result is sharp.

NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS WITH SHARED VALUES

We obtain some normality criteria of families of meromorphic functions sharing values related to Hayman conjecture, which improves some earlier related results.

Cut-off value of glycated hemoglobin A1c for detecting diabetic retinopathy in the Chinese population

BACKGROUND Glycated hemoglobin A1c(HbA1c)is considered the most suitable for diabetes mellitus diagnosis due to its accuracy and convenience.However,the effect of HbA1c on diabetic retinopathy(DR)in the Han and Korean populations in Jilin,China,remains inconclusive.AIM To determine the best cut-off of HbA1c for diagnosing DR among the Chinese.METHODS This cross-sectional study included 1933 participants from the Yanbian area of Jilin Province,China.Trained investigators employed a questionnaire-based survey,physical examination,laboratory tests,and fundus photography for the investigation.The best cut-off value for HbA1c was established via the receiver operating characteristic curve.The factors associated with HbA1c-associated risk factors were determined via linear regression.RESULTS The analysis included 887 eligible Chinese Han and Korean participants,591 of whom were assigned randomly to the training set and 296 to the validation set.The prevalence of DR was 3.27% in the total population.HbA1c of 6.2% was the best cut-off value in the training set,while it was 5.9% in the validation set.In both Chinese Han and Korean populations,an HbA1c level of 6.2% was the best cut-off value.The optimal cut-off values of fasting blood glucose(FBG)≥7 mmol/L and<7 mmol/L were 8.1% and 6.2% respectively in Han populations,while those in Korean populations were 6.9%and 5.3%,respectively.Age,body mass index,and FBG were determined as the risk factors impacting HbA1c levels.CONCLUSION HbA1c may serve as a useful diagnostic indicator for DR.An HbA1c level of 6.2% may be an appropriate cut-off value for DR detection in the Chinese population.

Normal families and shared values of meromorphic functions

We studied the normality conditions in families of meromorphic functions, improved the results of Fang and Zalcman [Fang ML, Zalcman L, Normal families and shared values of meromorphic functions, Computational Methods and Function Theory, 2001, 1 （1）： 289-299], and generalized two new normality criterions. Let F be a family of meromorphic functions in a domain D, a a non-zero finite complex number, B a positive real number, and k and m two positive integers satisfying m〉2k＋4. If every function denoted by f belonging to F has only zeros with multiplicity at least k and satisfies f^m（z）f^（k）（Z）=α→ ｜^f（k）（z）｜ ≤B or f^m（z）f^（k）（z）=α→｜f（z）｜ ≥, then F is normal in D.

Cut-off Values of Diagnostic Indices to Detect Iron Deficiency in Chinese Breast-fed Infants

Iron deficiency anemia is one of the most prevalent nutritional deficiency worldwide. The commonly used cut-off values for identifying iron deficiency are extrapolated from older children and may not be suitable for infants. Therefore, our study aimed to establish appropriate cut-off values for the evaluation of iron status in Chinese infants. Pregnant women who delivered at 〉37 gestational weeks with normal iron status were recruited. Later, infants with normal birth weight and who were breastfed in the first 4 months were selected. Blood samples were collected to assess hemoglobin, serum ferritin, soluble transferrin receptor, mean corpuscular volume and free erythrocyte protoporphyrin. Cut-offs of all iron indices were determined as the limit of 95% confidence interval.

Normal Functions Concerning Shared Values

In this paper we discuss normal functions concerning shared values. We obtain the follow result. Let F be a family of meromorphic functions in the unit disc A, and a be a nonzero finite complex number. If for any f ∈F, the zeros of f are of multiplicity, f and f′ share a, then there exists a positive number M such that for any f∈F1（1-｜z｜^2） ｜f′（z）｜/1＋｜f（z）｜^2≤M.

Normal Criteria and Shared Values by Differential Polynomials

For a family of meromorphic functions on a domain D, it is discussed whether F is normal on D if for every pair functions f(z),g∈F , f'–afnand g'–agn share value d on D when n=2,3, where a, b are two complex numbers, a≠0,∞,b≠∞.Finally, the following result is obtained:Let F be a family of meromorphic functions in D, all of whose poles have multiplicity at least 4 , all of whose zeros have multiplicity at least 2. Suppose that there exist two functions a(z) not idendtically equal to zero, d(z) analytic in D, such that for each pair of functions f and in F , f'–a(z)f2 and g'–a(z)g2 share the function d(z) . If a(z) has only a multiple zeros and f(z)≠∞ whenever a(z)=0 , then F is normal in D.

Normal values of flash visual evoked potentials in rabbits: Differences between the sexes and the eyes

BACKGROUND: The wave form, latency and wave amplitude of visual evoked potentials (VEP) are obviously affected by the stimulative parameters, physiological status of the subjects and anesthetics, thus there are greater normal variations and individual differences. The features of flash VEP (F-VEP) are to be observed. OBJECTIVE: To observe and compare the differences of F-VEP latencies and wave amplitudes between eyes in rabbits, and investigate the correlation with sex and the side of eyes. DESIGN: A comparative animal experiment. SETTING: Department of Neurosurgery, General Hospital of Chinese PLA. MATERIALS: The experiment was carried out in the neurophysiological laboratory of the Institute of Neurosciences, General Hospital of Chinese PLA from September 2004 to February 2005. Thirty big-ear rabbits of clean degree, 15 males and 15 females, weighing 2.0-2.5 kg, were provided by the animal center of the General Hospital of Chinese PLA. METHODS: Viking-IV perioperative monitor and flash stimulator for special use were applied. The rabbits were anesthetized with intramuscular injection of compound ketamine. The recording electrode was placed at 3 mm anterior to exoccipital tuberosity (onion, Oz), and the reference electrode was placed at the ear edge of the same side. The stimulative frequency was 1.9 Hz, and the amplifier was 50 μV; The range of wave filter was 5 Hz for high pass and 100 Hz for low pass; The average overlapping was 200 times, and the analytical time was 250 ms. MAIN OUTCOME MEASURES: Comparison of F-VEP wave forms; F-VEP latencies and wave amplitudes. RESULTS: All the 30 rabbits were involved in the analysis of results. ① Comparison of F-VEP wave forms in rabbits: The F-VEP waves mainly manifested as positive-negative-positive (PNP). The F-VEP manifestations to light stimulations were extremely similar between left and right eyes, and the wave amplitudes of both eyes were obviously increased. ② Determinations of F-VEP latencies and wave amplitudes: There were no significant differences in the latencies and wave amplitudes of F-VEP between the two groups (P > 0.05), the latencies of P1, N1 and P2 waves of left eye were (32.59±2.01), (43.85±4.35) and (66.20±8.13) ms, respectively, and the wave amplitudes of P1, N1 and P2 waves of left eye were (16.45±10.22), (7.93±3.56) and (17.62±8.18) μV. F-VEP latencies were stable with small changes, whereas amplitudes had greater changes. CONCLUSION: ① The latency and wave amplitudes F-VEP were stable with good repetition. ② The latencies and wave amplitudes had no significant differences between males and females, as well as between left and right eyes. Further investigation should be undertaken on the animal and clinical field.

Dynamic monitoring of menopause hormone therapy and defining the cut-off value of endometrial thickness during uterine bleeding

The aim of this study was to evaluate the effects of low-dose tibolone therapy on ovarian area, uterine volume and endometrial thickness, and define the cut-off value of endometrial thickness for curettage during uterine bleeding. We followed 619 postmenopausal women, aged 40-60 years, for two years. There were 301 subjects in the low-dose tibolone treatment group and 318 subjects in the control group. The ovarian area, uterine volume and endometrial thickness in all participants were measured by transvaginal ultrasound prior to, one and two years post enrollment, respectively. Endometrial specimens were collected from all subjects with abnormal uterine bleeding during the follow-up period. We found that the uterine volume in the treatment group was greater than that in the control group, and the difference was significant （P〈0.05）, but there were no significant differences in ovarian area and endometrial thickness between the two groups （P〉0.05）. When the cut-off value for endometrial thickness was 7.35 ram, the sensitivity and specificity were 100% and 79.07%, respectively, and 85.71% and 93.02% when 7.55 mm was set as the cut-offduring tibolone therapy. The results indicate that low-dose tibolone therapy may postpone uterine atrophy and the cut-off value of endometrial thickness may be appropriately adjusted for curettage.

Normal Reference Value of Red Blood Cell Count of Chinese Presenile Men and Geographical Factors

This paper aims at providing a scientific basis for unifying the normal reference value standards of red blood cell count of Chinese presenile men. The paper, using microscopical counting method, studies the relationship between the normal reference values of 38,061 samples of red blood cell count of presenile men and eight geographical factors in 297 units in China. It is found that the correlation of geographical factors and the normal reference value of red blood cell count of presenile men is quite significant （F=303.00, P=-0.000）. By using the method of stepwise regression analysis, one regression equation is inferred. It is concluded that if geographical data are obtained in a certain area, the normal reference value of red blood cell count of presenile men in this area can be reckoned by using the regression analysis. Furthermore, according to the geographical factors, China can be divided into eight regions： Northeast China Region, North China Region, Shanxi-Shaanxi-Irmer Mongolia Region, Middle and Lower Reaches of the Changjiang River Region, Southeast China Region, Northwest China Region, Southwest China Region and Qinghai-Tibet Plateau Region.

Normality and Shared Value Concerning Differential Polynomials

Let F be a family of functions meromorphic in a domain D, let m, n k , k be three positive integers and b be a finite nonzero complex number. Suppose that, (1) for eachf∈F, all zeros of f have multiplicities at least k ; (2) for each pair of functions f, g ∈F,P(f)H(f) and P(g)H(g) share b, where P(f) and H(f) were defined as (1.1) and (1.2) and nk ≥ max 1≤i≤k-1 {n i }; (3) m ≥ 2 or nk ≥ 2, k ≥ 2, then F is normal in D.

Multifractal estimation of NMR T_(2) cut-off value in low-permeability rocks considering spectrum kurtosis: SMOTE-based oversampling integrated with machine learning

The transverse relaxation time (T_(2)) cut-off value plays a crucial role in nuclear magnetic resonance for identifying movable and immovable boundaries, evaluating permeability, and determining fluid saturation in petrophysical characterization of petroleum reservoirs. This study focuses on the systematic analysis of T_(2) spectra and T_(2) cut-off values in low-permeability reservoir rocks. Analysis of 36 low-permeability cores revealed a wide distribution of T_(2) cut-off values, ranging from 7 to 50 ms. Additionally, the T_(2) spectra exhibited multimodal characteristics, predominantly displaying unimodal and bimodal morphologies, with a few trimodal morphologies, which are inherently influenced by different pore types. Fractal characteristics of pore structure in fully water-saturated cores were captured through the T_(2) spectra, which were calculated using generalized fractal and multifractal theories. To augment the limited dataset of 36 cores, the synthetic minority oversampling technique was employed. Models for evaluating the T_(2) cut-off value were separately developed based on the classified T_(2) spectra, considering the number of peaks, and utilizing generalized fractal dimensions at the weight <0 and the singular intensity range. The underlying mechanism is that the singular intensity and generalized fractal dimensions at the weight <0 can detect the T_(2) spectral shift. However, the T_(2) spectral shift has negligible effects on multifractal spectrum function difference and generalized fractal dimensions at the weight >0. The primary objective of this work is to gain insights into the relationship between the kurtosis of the T_(2) spectrum and pore types, as well as to predict the T_(2) cut-off value of low-permeability rocks using machine learning and data augmentation techniques.

INTERSECTION POINT RULE OF THE RETENTION VALUE AND NORMAL BOILING POINT OF THE HOMOLOGUES IN REVERSED-PHASE HIGH-PERFORMANCE LIQUID CHROMATOGRAPHY

In this paper, a linear relationship between the logarithm of capacity factor k and normal boiling point to of the homologues has been derived, based on the basic retention equation of liquid chromatography according to statistical thermodyoamics proposed by professor Ln Peizhang and others, This equation has been verified by a large number of experimental data, all the strsight lines of lnk- of bumologues for different mobile phass coaiposltion cross each other at the same point, So the intereection point equation van proposed, wbich was used to prodict the retention valu, the result was satisfactory.

Riemann Boundary Value Problem of Non-Normal Type on the Infinite Straight Line

Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1-8]. The main ap- proach is to use the decomposition of polyanalytic functions and their generalization to transform the boundary value problems to their corresponding boundary value problems for analytic functions. Recently, inverse Riemann BVPs for generalized analytic functions or bianalytic functions have been investigated in [9-12]. In this paper, we consider a kind of Riemann BVP of non-normal type on the infinite straight line and discuss the solvable conditions and the general solution for it.

Normal reference value of forced vital capacity of Chinese younger women and geographical factors

Objective To supply a scientific basis for standardizing the normal reference value of forced vital capacity(FVC)of Chinese younger women.Methods We studied the relationship between the normal reference value of 21767 samples of FVC of younger women and eight geographical factors in 157 areas in China.Results It was found that the correlation between geographical factors and the normal reference value of FVC of younger women was quite significant(F=5.884,P=0.000).By adopting the method of mathematical regression analysis,one regression equation was inferred:=3.146+0.00006919X1+0.01315X4-0.006966X6+0.09524X8±0.254.In the above equation,is the normal reference value of younger women’ FVC(L);X1 is the altitude(m);X4 is the annual mean air temperature(℃);X6 is the annual mean relative humidity(%);X8 is the annual mean wind speed(m/s);0.254 is the value of the residual standard deviation.Conclusion If geographical values are obtained in a certain area,the normal reference value of FVC of younger women in this area can be obtained by using the regression equation.Furthermore,according to the geographical factors,China can be divided into eight regions:Northeast China Region,North China Region,Shanxi-Shaanxi-Inner Mongolia Region,middle and lower reaches of the Yangzte River Region,Southeast China Region,Northwest China Region,Southwest China Region,and Qinghai-Tibet Plateau Region.

The Value Distribution and Normality Criteria of a Class of Meromorphic Functions

In this article,we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values,which improves some earlier related results.

STUDYING THE FOCAL VALUE OF ORDINARY DIFFERENTIAL EQUATIONS BY NORMAL FORM THEORY

We present a new method to calculate the focal value of ordinary differential equation by applying the theorem defined the relationship between the normal form and focal value,with the help of a symbolic computation language M ATHEMATICA,and extending the matrix representation method.This method can be used to calculate the focal value of any high order terms.This method has been verified by an example.The advantage of this method is simple and more readily applicable.the result is directly obtained by substitution.

Wild-type MIC Distribution and Epidemiological Cut-off Value and Resistant Characteristics of Colistin Against Escherichia Coli from Chickens

The aim of the present study was to investigate minimum inhibitory concentration(MIC)distributions by broth microdilution(BMD)method and to determine the preliminary epidemiological cut-off value(ECV)of colistin by epidemiological cut-off(ECOFF)finder against E.coli from chickens in China.Anal swabs were collected from chicken farms in China.BMD method was used to measure MIC50 and MIC90 of colistin which were 2 and 4μg•mL^(-1),respectively.MIC frequency distributions for colistin were used to estimate preliminary ECV(8μg•mL^(-1)).High percentages of resistance to ampicillin(94.12%),nalidixic acid(94.12%),enrofloxacin(94.12%),tetracycline(94.12%),ciprofloxacin(88.24%),florfenicol(88.24%),neomycin(64.71%),gentamicin(58.82%),levofloxacin(58.82%),doxycycline(88.24%)and cefalexin(76.47%)were found.In addition,low percentages of resistance to amikacin(5.88%),spectinomycin(17.65%)and fosfomycin(41.18%)were noted.Notably,amoxicillin,sulfisoxazole and trimethoprim resulted in a 100%resistance generation efficacy rate.Prevalence of mcr-1 in E.coli(9/17)in chromosomal DNA was higher than mcr-4(2/17)gene,and mcr-1(5/17)was higher than mcr-4(3/17)in plasmid.

Singular Value Inequalities for Compact Normal Operators

We give singular value inequality to compact normal operators, which states that if is compact normal operator on a complex separable Hilbert space, where is the cartesian decomposition of , then Moreover, we give inequality which asserts that if?is compact normal operator, then .Several inequalities will be proved.

Analysis on preserving or increasing the value of social security funds under the new normal economy in China

The ＂new normal＂ is the current stage of development of China＇s economy. The ＂new＂ in new normal means different to past; the ＂normal＂ means relatively stable. For a period of time in the future, the decrease of potential growth rate has become an indisputable fact. Social security fund is an important source of funds for the protection of people＇s livelihood, whose every movement often attract much attention. Under the situation of new normal economy, how to ensure the preserving or increasing value of social security funds on the premise of security is the core task in the operations management of social security fund investment. At present, there are some difficulties in the development of the social security funds, such as the management system and operation mechanism are not perfect, some institutional measures have not been fully implemented and the progress of the law and regulations is slow. In this paper, we will put forward some corresponding improvement measures, such as expand the scope of social security fund investment, accelerate the implementation of the nominal account system and strengthen the actuarial management of social security fund.