ON THE NUMBER OF EULERIAN PLANAR MAPS

This paper presents the number of combinatorially distinct rooted Eulerian planar maps with the number of non-root-vertices and the number of non-root-faces as two parameters. The parametric expressions for determining the number in tha loopless Eulerian case are also obtained.

Mersenne Numbers, Recursive Generation of Natural Numbers, and Counting the Number of Prime Numbers

A simple recursive algorithm to generate the set of natural numbers, based on Mersenne numbers: MN = 2N – 1, is used to count the number of prime numbers within the precise Mersenne natural number intervals: [0;MN]. This permits the formulation of an extended twin prime conjecture. Moreover, it is found that the prime numbers subsets contained in Mersenne intervals have cardinalities strongly correlated with the corresponding Mersenne numbers.

Calculation and analysis of the number of return photons from sodium laser beacon excited by the long pulse laser with circular polarization

The number of return photons from sodium laser beacon（SLB） greatly suffers down-pumping, recoil, and geomagnetic field when the long pulse laser with circular polarization interacts with sodium atoms in the mesosphere. Considering recoil and down-pumping effects on the number of return photons from SLB, the spontaneous radiation rates are obtained by numerical computations and fittings. Furthermore, combining with the geomagnetic field effects, a new expression is achieved for calculating the number of return photons. By using this expression and considering the stochastic distribution of laser intensity in the mesosphere under different turbulence models for atmosphere, the number of return photons excited by the narrow-band single mode laser and that by the narrow-band three-mode laser are respectively calculated. The results show that the narrow-band three-mode laser with a specific spectrum structure has a higher spontaneous radiation rate and more return photons than a narrow-band single mode laser. Of note, the effect of the atmospheric turbulence on the number of return photons is remarkable. Calculation results indicate that the number of return photons under the HV5/7 model for atmospheric turbulence is much higher than that under the Greenwood and Mod HV models.

IS THE“DEGREE OF AGGREGATION”A FUNCTION OF THE AVERAGE AGGREGATE NUMBER,OR OF THE NUMBER OF AGGREGATES,OR BOTH?

Measurement of the average aggregate number of coaggregates(N_co)and evaluation Of the number of coaggregates([CoAg])in the region of increasing degree of aggregation shows that only N_co increases linearly with the concentration of the target molecules CE-In and BL-ol.

Factors Influencing the Number of Rabies Cases in Children in China

To understand the epidemic situation and factors influencing rabies cases in children in China, we obtained an overview of the current epidemic based on individual data of rabies cases in children and a descriptive analysis was carried on the prevalence and related factors. The results showed that the rabies cases in children accounted for 21.3% of the total number of rabies cases in China, 97.0% of these cases occurred in rural areas, they were mainly caused by dogs （81.5%）, and were primarily level Ill exposure （47.7%）. More than half of the cases were not treated with wound care, vaccination rate was extremely low （15.7%）, and only 5.9% of cases were injected with antibodies. Furthermore, 25.4% of cases adopted incorrect treatments such as extruding bleed and wound closure, cases vaccinated with 5 injections acco- unted for only 22.5%. In conclusion, the prevalence of rabies cases in children in China remains a serious concern, the number and immune status of dogs in rural areas, and knowledge of rabies by risk populations should be considered in future rabies prevention and control programs.

Annual change of the number of anaerobic sulf ite reducing bacteria in sediment of the Daya Bay

The surface sediment samples were collected month by month at nine stations in the Daya Bay from January to December 1987, and the number of anaerobic sulfite reducing bacteria and their spores and the regularity of seasonal change were determined. The effect of environmental factors, water temperature and the resoluble oxygen concentration in the bottom of seawater on the number of them were discussed. The results show that the number of anaerobic su|fite reducing bacteria were low in sediment of the Daya Bay, indicating that the hay was less contaminated.

The Number of Five Basic Elements' Motion of Traditional Chinese Medicine and Cancer Prediction

"The number of five basic elements'motion"varies according to the date of birth,which is tightly tied to human health.To predict cancer with"the number of five basic elements'motion"is simple,accurate,worth of research and popularizing.The theory of“five basic elements'motion and six climatic changes”is a key part of Traditional Chinese Medicine,“the number of five basic elements'motion”is strongly related to the physiology and pathology of human body.Combine with folk pathology prediction,“the number of five basic elements'motion”has been proved to have some scientific validity and of high accuracy in cancer prediction,it is worth to study,research and be discussed in-depth.

The Impact of Incentives on the Number of Suppliers

In the context of adulteration by suppliers,downstream firms need to choose between incentives and regulation to ensure product quality.Studies have shown that the adulteration behavior of suppliers increases with the degree of dispersion of suppliers,that is,the number of suppliers increases.Therefore,based on the assumption that the number of suppliers impacts quality uncertainty,this paper further introduces the number of suppliers into the incentive model to investigate the relationship between supply chain dispersion,that is,the number of suppliers,social integrity,and incentive strength.The study finds that the optimal number of suppliers depends on social integrity,regulatory cost,and incentive strength.There is a positive correlation between social integrity and the number of suppliers,while regulatory costs and incentive strength have a negative correlation with the number of suppliers.That means,the higher the social integrity,the lower the regulatory cost;and the lower the incentive intensity,the more optimal suppliers can be selected.

Method for determining number of coherent signals in the presence of colored noise

The approach of estimating the number of signals based on information theoretic criteria has good performance in the assumption of white noise, but it always leads to false estimation of the coherent sources in colored noise. An approach combining the combined information theoretic criteria and eigen- value correction, is presented to determine number of signals. The method uses maximum likelihood （ML） and information theoretic criteria to estimate coherent signals alternately, then eliminate the inequality of the eigenvalues caused by colored noise by correcting the noise eigenvalues. The computer simulation results prove the effective performance of the method.

A Study on Social Choice Making:the Number of Admissible Preference Orderings for SMV

In this paper, we study, mathematically speaking, the problem-the number of admissible preference orderings for the transitivity of simple majority vote(SMV) derived from Arrow’s Impossibility Theorem. In our research, we find, by computer enumerating, that some results given by Craven are not correct. By defining a set of constraints, we give the recurrence formula of the local maximal number of admissible preference orderings and some other useful results.

On the Number of Finite Non-isomorphic Abelian Groups in Short Intervals

Let the arithmetic function a(n) denote the number of non-isomorphic Abeliangroups of order n;k, positive integer, and x≥0. We setA_k(x)= sum from n≤x a(n)=k to (1)andA_k(x;h) =A_k(x+h)-A_k(x). A. Ivice first investigated the distribution of the values of finite non-isomorphicAbelian groups in short intervals. E. Kratzel reduced the problem to estimate theerror term △(1, 2, 3;x) in the three-dimensional multiplicative problem, and furtherimproved Ivice’s result.

CYCLE CONTR0L FUNCTIONS AND THE NUMBER 0F LIMIT CYCLES

The cycle coatrol function is defined and used to estimate tbe number of limit cycles for someplanar autonomous systems. Some sufficient conditions for the existence of no or at most one limitcycles are given.

Can Raising the Tobacco Tax Reduce the Number of Smokers?

Experts from China’s State Administration of Taxation and the University of California,Berkeley unveiled a report,"Tobacco Tax and Its Potential Impact on China,"

Studies of Structural and Thermodynamic Properties for Polychlorinated Thianthrenes by Density Functional Theory

The structural and thermodynamic （PCTAs） in the ideal gas state at 298.15 K and 1.013 properties of 75 polychlorinated thianthrenes ×10^5 Pa have been calculated at the B3LYP/6- 31G＊ level using Gaussian 98 program. Based on the output data of Gaussian, the isodesmic reactions were designed to calculate standard enthalpy of formation （△fH^θ） and standard free energy of formation （△fH^θ） of PCTAs congeners. The relations of these thermodynamic parameters with the number and position of C1 atom substitution （Npcs） were discussed, and it was found that there exists high correlation between thermodynamic parameters （total energy （TE）, zero-point vibrational energy （ZPE）, thermal correction to energy （Eth）, heat capacity at constant volume （Cv^θ）, entropy （S^θ）, enthalpy （H^θ）, free energy （G^θ）, standard enthalpies of formation （△fH^θ） and standard Gibbs energies of formation （△fG^θ）） and Npcs. On the basis of the relative magnitude of their △fG^θ, the order of relative stability of PCTA congeners was theoretically proposed. In addition, the correlations between structural parameters and Npcs were also discussed. The good correlations were found between molecular average polarizability （α）, energy of the highest occupied molecular orbital （EHOMO）, molecular volume （Vm） and Npcs, and all R^2 values are larger than 0.95. Moreover, it was supposed that the isomer groups with higher toxicity should be Tri-CTA and TCTA.

Studies of Thermodynamic Properties and Relative Stability of Polybrominated Xanthones by Density Functional Theory

The thermodynamic properties of xanthone（XTH） and 135 polybrominated xanthones（PBXTHs） in the standard state have been calculated at the B3LYP/6-31G＊ level using Gaussian 03 program.The isodesmic reactions were designed to calculate the standard enthalpy of formation（△fHθ） and standard free energy of formation（△fGθ） of PBXTH congeners.The relations of these thermodynamic parameters with the number and position of Br atom substitution（NPBS） were discussed,and it was found that there exist high correlation between thermodynamic parameters（entropy（Sθ）,△fHθ and △fGθ） and NPBS.According to the relative magnitude of their △fGθ,the relative stability order of PBXTH congeners was theoretically proposed.The relative rate constants of formation reactions of PBXTH congeners were calculated,Moreover,the values of molar heat capacity at constant pressure（Cp,m） from 200 to 1000 K for PBXTH congeners were also calculated,and the temperature dependence relation of them was obtained,suggesting very good relationships between Cp,m and temperature（T,T^1 and T^2） for almost all PBXTH congeners.

Does Success Breed Success?A Study on the Correlation between Impact Factor and Quantity in Chinese Academic Journals

Purpose:This paper studies the relationship between the impact factor(IF)and the number of journal papers in Chinese publishing system.Design/methodology/approach:The method proposed by Huang(2016)is used whereas to analysis the data of Chinese journals in this study.Findings:Based on the analysis,we find the following.(1)The average impact factor(AIF)of journals in all disciplines maintained a growth trend from 2007 to 2017.Whether before or after removing outlier journals that may garner publication fees,the IF and its growth rate for most social sciences disciplines are larger than those of most natural sciences disciplines,and the number of journal papers on social sciences disciplines decreased while that of natural sciences disciplines increased from 2007 to 2017.(2)The removal of outlier journals has a greater impact on the relationship between the IF and the number of journal papers in some disciplines such as Geosciences because there may be journals that publish many papers to garner publication fees.(3)The success-breeds-success(SBS)principle is applicable in Chinese journals on natural sciences disciplines but not in Chinese journals on social sciences disciplines,and the relationship is the reverse of the SBS principle in Economics and Education&Educational Research.(4)Based on interviews and surveys,the difference in the relationship between the IF and the number of journal papers for Chinese natural sciences disciplines and Chinese social sciences disciplines may be due to the influence of the international publishing system.Chinese natural sciences journals are losing their academic power while Chinese social sciences journals that are less influenced by the international publishing system are in fierce competition.Research limitation:More implications could be found if long-term tracking and comparing the international publishing system with Chinese publishing system are taken.Practical implications:It is suggested that researchers from different countries study natural science and social sciences journals in their languages and observe the influence of the international publishing system.Originality/value:This paper presents an overview of the relationship between IF and the number of journal papers in Chinese publishing system from 2007 to 2017,provides insights into the relationship in different disciplines in Chinese publishing system,and points out the similarities and differences between Chinese publishing system and international publishing system.

工件允许拆分加工的单机排序问题

The single-machine lot scheduling problem with splittable jobs to minimize the number of tardy jobs has been showed to be weakly NP-hard in the literature.In this paper,we show that a generalized version of this problem in which jobs have deadlines is strongly NP-hard,and also present the results of some related scheduling problems.

Analysis of the outbreak of COVID-19 in Japan by SIQR model

The SIQR model is exploited to analyze the outbreak of COVID-19 in Japan where the number of the daily confirmed new cases is explicitly treated as an observable.It is assumed that the society consists of four compartments;susceptible individuals(S),infected individuals at large(I),quarantined patients(Q)and recovered individuals(R),and the time evolution of the pandemic is described by a set of ordinary differential equations.It is shown that the quarantine rate can be determined from the time dependence of the daily confirmed new cases,from which the number of infected individuals can be estimated.The infection rate and quarantine rate are determined for the period from mid-February to mid-April in Japan and transmission characteristics of the initial stages of the outbreak in Japan are analyzed in connection with the policies employed by the government.The effectiveness of different measures is discussed for controlling the outbreak and it is shown that identifying patients through PCR(Polymerase Chain Reaction)testing and isolating them in a quarantine is more effective than lockdown measures aimed at inhibiting social interactions of the general population.An effective reproduction number for infected individuals at large is introduced which is appropriate to epidemics controlled by quarantine measures.

Finite p-Groups with Few Non-major k-Maximal Subgroups

A subgroup of index p^k of a finite p-group G is called a k-maximal subgroup of G.Denote by d(G) the number of elements in a minimal generator-system of G and by δ_k(G) the number of k-maximal subgroups which do not contain the Frattini subgroup of G.In this paper,the authors classify the finite p-groups with δ_(d(G))(G) ≤ p^2 and δ_(d(G)-1)(G) = 0,respectively.

Almost automorphically-forced flows on S^(1) or R in one-dimensional almost periodic semilinear heat equations

In this paper,we consider the asymptotic dynamics of the skew-product semiflow generated by the following time almost periodically-forced scalar reaction-diffusion equation:u_(t)=u_(xx)+f(t,u,u_(x)),t>0,0<x<L(0.1)with the periodic boundary condition u(t,0)=u(t,L),u_(x)(t,0)=u_(x)(t,L),(0.2)where f is uniformly almost periodic in t.In particular,we study the topological structure of the limit sets of the skew-product semiflow.It is proved that any compact minimal invariant set(throughout this paper,we refer to it as a minimal set)can be residually embedded into an invariant set of some almost automorphically-forced flow on a circle S^(1)=R/LZ(see Definition 2.4 for“residually embedded”).Particularly,if f(t,u,p)=f(t,u,-p),then the flow on a minimal set can be embedded into an almost periodically-forced minimal flow on R(see Definition 2.4 for“embedded”).Moreover,it is proved that the ω-limit set of any bounded orbit contains at most two minimal sets that cannot be obtained from each other by phase translation.In addition,we further consider the asymptotic dynamics of the skew-product semiflow generated by(0.1)with the Neumann boundary condition u_(x)(t,0)=u_(x)(t,L)=0 or the Dirichlet boundary condition u(t,0)=u(t,L)=0.For such a system,it has been known that theω-limit set of any bounded orbit contains at most two minimal sets.By applying the new results for(0.1)+(0.2),under certain direct assumptions on f,we prove in this paper that the flow on any minimal set of(0.1)with the Neumann boundary condition or the Dirichlet boundary condition can be embedded into an almost periodically-forced minimal flow on R.Finally,a counterexample is given to show that even for quasi-periodically-forced equations,the results we obtain here cannot be further improved in general.