Scheme to measure the expectation value of a physical quantity in weak coupling regime

In quantum mechanics, the expectation value of an operator can be measured by using the projective measurement, ifthe coupling between the measured system and pointer is strong enough. However in the weak coupling regime, the pointercan not show all the eigenvalue of the physical quantity directly due to the overlapping among the pointer states, whichmakes the measurement of the expectation value difficult. In this paper, we propose an expectation value measurementmethod in the weak coupling regime inspired by the weak measurement scheme. Compared to the projective measurement,our scheme has two obvious advantages. Experimentally we use the internal state and motional state of a single trapped40Ca+ to establish the measurement scheme and realize the proof of principle demonstration of the scheme.

Children's expectancy beliefs and subjective task values through two years of school-based program and associated links to physical education enjoyment and physical activity

Purpose：The present study examined the patterns of children＇s expectancy beliefs and subjective task values through the Physical Activity as Civil Skill Program and associated links to physical education enjoyment and total physical activity.Methods：The sample comprised 401 children aged 9–13 years from 3 small towns located in North-East Finland.All children received school-based activities across 2-year program from Grades 5 to 7.The present data were collected using questionnaires across 3 measurement phases during 2012–2014.Results：The levels of expectancy beliefs and subjective task values indicated to be relatively high and the development was stable through the program,especially in terms of expectancy beliefs,attainment value,and cost.In contrast,interest value and utility value decreased over the particular period of time.Boys believed they are physically more competent when compared to other students and valued physical education classes more important than girls.In addition,the higher the physical activity level the children reported,the higher the physical education enjoyment they perceived.Conclusion：The current program including actions to increase physical activity through manipulation of psychological and physical school environment modification indicated to be an effective strategy to prohibit declining levels of children＇s expectancy beliefs and task values.

On the Expected Present Value of Total Dividends in a Risk Model with Potentially Delayed Claims

In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for K n claim amount distributions. Numerical illustrations are also given.

OPTIMAL REINSURANCE UNDER EXPECTED VALUE PRINCIPLE

The paper concerns the problem how to purchase the reinsurance in order to make the insurer and the reinsurance company＇s total risk to be least under the expected value principle. When the insurer and reinsurance company take arbitrary risk measures, sufficient con- ditions for optimality of reinsurance contract are given within the restricted class of admissible contracts. Further, the explicit forms of optimal reinsurance contract under several special risk measures are given, and the method to decide parameters as well.

Three Methods to Calculate the Financial Risk Measurement: Value- At-Risk and Expected Shortfall

This paper analyzes the relationship between the risk factor of each stock and the portfolio’s risk based on a small portfolio with four U.S.stocks,and the reason why these risk factors can be regarded as a market invariant.Then,it evaluates the properties of the convex and coherent risk indicators of the capital requirement index composed of VaR and ES,and use three methods(the historical estimation method,boudoukh’s mixed method and Monte Carlo method)to estimate the risk measurement indicators VaR and ES respectively based on the assumption of multivariate normal distribution’risk factors and multivariate student t-copula distribution’s one,finally it figures out that these three calculation results are very close.

Estimating the expected value of multiple prospects in bidding blocks

In recent years,China has accelerated the reform of its oil and gas management system,especially in competitive transfer of mining rights.Evaluating the expected value(EV)of lease blocks is crucial for the bidding decision of oil companies.When bidding for a block with several individual prospects,the simple addition of each prospect EV usually leads to overly high and optimistic resource volume and value estimates.For the assessment of the EV of a multi-prospect block,two factors should be considered.Firstly,the geological setting of the prospects,including their relative spatial relationship,their chance of geological success,their resources and their geological dependency,etc.The second factor is the exploration strategy of oil companies,concerned with the dry hole tolerance,the committed wells and the drilling priorities for the prospects,etc.A probabilistic method to assess the EV of a multi-prospect block is proposed,which proves to be favorable for formulating a bidding strategy for oil companies.In addition,a case study on two specific blocks with several prospects is presented to illustrate the effect of the above mentioned factors on the EV.

A Note on the Expectation Value of Time

In this note, the expectation value of time based on quantum mechanics formalism is derived. It is found that the expectation value of time does not depend on space.

EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER

This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo＇s derivative{C0D^δtu（t）=g（t,u（t））,0〈t〈1,1〈δ〈2,u（0）α≠0,u（1）=β≠0.

Measuring Recreational Value of World Heritage Sites Based on Contingent Valuation Method:A Case Study of Jiuzhaigou

World heritage possesses various kinds of use value and non-use value. Measuring the recreational value of world heritage sites is a key issue in the heritage tourism. This paper employs Contingent Valuation Method (CVM), which is an evaluation instrument on the basis of tourists′ attitude and preference, to measure the recreational value of Jiuzhaigou, one of the World Natural Heritage sites in China, and analyzes the biases in the survey. The results show that: 1) In 2009, Jiuzhaigou′s recreational value was 3.46×108 yuan (RMB), and the per capita Willingness to Pay (WTP) was 137.31 yuan by CVM. Compared with the results of other methods, this result is significantly low. 2) Among the factors that influence Jiuzhaigou tourists′ WTP, psychological perception factors have the greatest effect while demographic and socio-economic characteristics have a small effect on WTP. 3) The virtuality in CVM creates biases both from CVM itself and in the procedures that CVM was implemented. The former includes hypothetical bias, information bias, protest response bias, and strategic bias; and the latter includes the questionnaire design, population and sample definition, sampling and data processing. The paper analyses those biases and illustrates their potential in-fluences on the accuracy of CVM measurement. 4) Although there are various defects in CVM measurement, it is still an effective valuation method.

EXISTENCE OF SOLUTION FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

This paper is concerned with the boundary value problem of a nonlinear fractional differential equation. By means of Schauder fixed-point theorem, an existence result of solution is obtained.

STRONG LIMIT THEOREMS FOR EXTENDED INDEPENDENT RANDOM VARIABLES AND EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATIONS

Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have attracted a lot of interest recently.The purpose of this paper is to study the strong law of large numbers and the law of the iterated logarithm for a sequence of random variables in a sub-linear expectation space under a concept of extended independence which is much weaker and easier to verify than the independence proposed by Peng[20].We introduce a concept of extended negative dependence which is an extension of the kind of weak independence and the extended negative independence relative to classical probability that has appeared in the recent literature.Powerful tools such as moment inequality and Kolmogorov’s exponential inequality are established for these kinds of extended negatively independent random variables,and these tools improve a lot upon those of Chen,Chen and Ng[1].The strong law of large numbers and the law of iterated logarithm are also obtained by applying these inequalities.

Optimal b value of diffusion-weighted imaging on a 3.0T magnetic resonance scanner in Crohn's disease

AIM: To determine the optimal b value of diffusion-weighted imaging for detecting active inflammation in Crohn’s disease.

Assessment of self- and cross-absorbed SAF values for HDRK-man using GEANT4 code: internal photon and electron emitters

The ultimate need to account for the partial amount of energy deposited in target tissue/organ resulting from internal inhalation,ingestion,and injection intakes of radionuclides,defined by the Medical Internal Radiation Dosimetry committee as the specific absorbed fraction(SAF),has become obvious.In this study,we assessed the SAF values for self-and cross-absorption,which were calculated for a uniform distribution of monoenergetic photon and electron emitters with energies ranging from 15 keV to 3 MeV.The voxelized human phantom‘‘High-Definition Reference Korean-man’’(HDRK-man),which was implemented using the Monte Carlo simulation code GEANT4(version 10.1),was used for several combinations of target–source organs.The results were compared to those of the International Commission on Radiological Protection Reference(ICRP133)and Zubal phantoms.It was found that the SAF values of the three models have a similar trend.However,the SAF values for the HDRK-man phantom were higher than those of the other two models,with a relatively good agreement with those for the ICRP133 phantom(differences of 13.9±2.8 and 12.1±3.2 for photon and electron emitters,respectively).To analyze the differences in SAF values,we calculated the chord length distributions(CLDs)for selected target–source combinations.The parameters of organ mass(or volume)and CLDs,in addition to the adopted computational procedures,mainly cause such discrepancies.For realistic radionuclide emission spectra,an overall overestimation was observed when computing the S values for three radiopharmaceuticals studied(I-131,In-111,and Lu-177)and for liver–spleen intra-and inter-organ absorption when compared with published data.The new arrangement of S and SAF values is expected to add value for multidisciplinary research and clinical communities.

Davis's Inequalities for Two-Parameter Banach Space Valued Strong Martingales and Geometrical Properties of Banach Spaces

In this paper we investigated theL 1 norm inequalities of theP square and the maximal functions of two-parameterB-valued strong martingales, which can be applied to characterizep-smoothness andq-convexity of Banach spaces.

Does the EVA valuation model explain the market value of equity better under changing required return than constant required return?

Through the Economic-Value-Added(EVA)valuation model,the expected market value of equity can be determined by adding the book value of equity with the present value of expected EVAs under the assumption of constant required return and constant return on equity.The equation of EVA valuation model has taken its shape under the assumption of constant required return and constant return on equity.However,a large body of empirical evidence indicates that required rate of return never remain constant.The EVA-valuation model formulated under constant required return cannot be implemented under the scenario of changing required return.In this study,we explored whether the EVA valuation model could be implemented under changing required return by making any changes in the model and found that it could be implemented under the scenario of changing required return by replacing the book value of the equity of the existing model with the present value of required earnings or normal market earnings.We further examined whether the explanatory ability of the EVA valuation model under the assumption of changing required return is better than that of the valuation model under the assumption of constant required return.Relative information content analyses were conducted by considering sample of the intrinsic value of equities determined by valuation models and the market value of equities of 69 large-cap,88 mid-cap,and 79 small-cap companies.The results showed that the EVA-based valuation model with changing normal market return outperformed the EVA-based valuation model with constant required return.

Q value of anelastic S-wave attenuation in Yunnan region

The study of seismic attenuation property is a major subject in seismology. Seismic waves recorded by seismic stations （seismographs） contain source effect, seismic wave propagation effect, site response of seismic stations and instrumental response. The path effect of seismic wave propagation, site response of seismic stations and instrumental response must be taken out in the study of source property with seismic data. The path effect of seismic wave propagation （seismic attenuation） involves an important influential factor, the anelastic attenuation of medium, which is measured with quality factor Q, apart from geometric attenuation with the distance. As a basic physical parameter of the Earth medium, Q value is essential for quantitative study of earthquakes and source property （e.g. determination of source parameters）, which is widely used in earthquake source physics and engineering seismology.

On Accelerated Singular Value Thresholding Algorithm for Matrix Completion

An accelerated singular value thresholding (SVT) algorithm was introduced for matrix completion in a recent paper [1], which applies an adaptive line search scheme and improves the convergence rate from O(1/N) for SVT to O(1/N2), where N is the number of iterations. In this paper, we show that it is the same as the Nemirovski’s approach, and then modify it to obtain an accelerate Nemirovski’s technique and prove the convergence. Our preliminary computational results are very favorable.

BOREL'S DIRECTIONS AND SHARED VALUES

In this article, we study the problems of Borel＇s directions of meromorphic func- tions concerning shared values and prove that if two meromorphie functions of infinite order share three distinct values, their Borel＇s directions are same.

Existence of Positive Solutions for a Third-Order Multi-Point Boundary Value Problem

By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous boundary value problem (BVP1): where for The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative .

Resolution of Grandi’s Paradox as Extended to Complex Valued Functions

Grandi’s paradox, which was posed for a real function of the form 1/(1+ x), has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function 1/(1+ ex ) . Grandi-type complex valued functions such as 1/(i + x) are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.