The Average Value Inequality in Sequential Effect Algebras

A sequential effect algebra （E, 0, 1, ,o） is an effect algebra on which a sequential product o with certain physics properties is defined; in particular, sequential effect algebra is an important model for studying quantum measurement theory. In 2005, Gudder asked the following problem： If a, b E （E, 0, 1, , o） and a⊥b and a o b⊥a o b, is it the case that 2（a o b） ≤ a2 b2 ？ In this paper, we construct an example to answer the problem negatively.

A comparison of tectonic ambient shear stress value in China with that in western USA

A method is proposed to estimate average tectonic ambient shear stress value for a region. Thus the average stress values of 19 regions in western USA, and 43 regions (each region is 1010) in Chinese mainland and its surroundings have been obtained. The data of 15 993 earthquakes are from the Internet Centroid Moment Tensor solution made by Harvard University from 1997 to 1999. The results demonstrate that there are highest average stress values in the regions of south California of USA and its off coast sea, reach to 12.0 MPa and 13.7 MPa respectively, then gradually decrease toward north, south, and east. The lowest value is 8.7 MPa and 63% of highest value. The average stress values in northern Xinjiang and in the Chayu region of Tibet are 17.2 and 12.9 MPa respectively. They are highest values in China and higher than USAs. The average stress value in North China, Yunnan, Sichuan, Taiwan is similar to south California of USA. The average stress value in South-North seismic zone is about 13 MPa, a little higher than south California. The distribution of average stress value for two important regions provides basic data for geology. These results are useful to research earthquake activity background and attenuation relation of strong ground motion parameters (e.g. peak acceleration and response spectra).

Main Patterns of Geochemistry of Phosphorus

The paper presents the main conclusions of the Russian monograph “Geochemistry of Phosphorus” (2020). Based on statistical processing of ~6100 sample averages (from ~190,000 analyses), new estimations of World averages (Clarke values) for Р2O5, % (and P, %), phosphorus-titanium module (P2О5/TiO2), phosphorus-calcium module (P2O5/CaO), phosphorus-iron module (P2О5/Fe2O3), and phosphorus-total iron module (P2O5/Fe2O3 + FeO). Many estimates have been made for the first time. In addition to the new Clarke estimates, sometimes very different from previous ones, the work carried out has led to a number of new conclusions. In particular, the titanium geochemical barrier for phosphorus has been first estimated, all the 11 genotypes of phosphogenesis have been named and characterized, five genetic correlations of phosphogenesis have been described, lithochemistry methods have been successfully applied to characterize the phosphorites. Due to the large breadth of generalization, the monograph has a large theoretical and applied value.

Location of Tibetan earthquakes──a nonlinear approach by a simplex optimized technique

An advanced earthquake location technique presented by Prugger and Gendzwill (1988) was introduced in this paper. Its characteristics are: 1) adopting the difference between the mean value by observed arrival times and the mean value by calculated travel times as the original reference time of event to calculate the traveltime residuals, thus resulting in the 'true' minimum of travel-time residuals; 2) choosing the L1 norm statistic of the residuals that is more suitable to earthquake location; 3) using a simplex optimized algorithm to search for the minimum residual value directly and iteratively, thus it does not require derivative calculations and avoids matrix inversions, it can be used for any velocity structures and different network systems and can solve out hypocentral parameters (λ, ,h) rapidly and exactly; 4) original time is further derived alone, so the trade-off between focal depth and original time is avoided. All these prominent features make us obtain more accurate Tibetan earthquake locations in the rare network condition by using this method. In this paper, we examined these schemes for our mobile and permanent networks in Tibet with artificial data sets,then using these methods, we determined the hypocentral parameters of partial events observed in the field work period of this project from July 1991 to September 1991 and the seven problematic earthquakes during 1989 - 1990. The hypocentral location errors may be estimated to be less than 3. 6 km approximately. The events with focal depth more than 40 km seem to be distributed in parallel to Qinghai-Sichuan-Yunnan arc structural zone.

Wiener Indices in Random Cyclooctane Chains

The Wiener index of a connected graph（molecule graph） G is the sum of the distances between all pairs of vertices of G. In this paper, simple exact formula are established for the expected value of Wiener index in random cyclooctane chain. Moreover, we obtain the average value of the Wiener indices with respect to the set of all cyclooctane chains with n octagons.

Estimation of Postmortem Interval Using the Radiological Techniques,Computed Tomography:A Pilot Study

Estimation of postmortem interval(PMI)has been an important and difficult subject in the forensic study.It is a primary task of forensic work,and it can help guide the work in field investigation.With the development of computed tomography(CT)technology,CT imaging techniques are now being more frequently applied to the field of forensic medicine.This study used CT imaging techniques to observe area changes in different tissues and organs of rabbits after death and the changing pattern of the average CT values in the organs.The study analyzed the relationship between the CT values of different organs and PMI with the imaging software Max Viewer and obtained multiparameter nonlinear regression equation of the different organs,and the study provided an objective and accurate method and reference information for the estimation of PMI in the forensic medicine.In forensic science,PMI refers to the time interval between the discovery or inspection of corpse and the time of death.CT,magnetic resonance imaging,and other imaging techniques have become important means of clinical examinations over the years.Although some scholars in our country have used modem radiological techniques in various fields of forensic science,such as estimation of injury time,personal identification of bodies,analysis of the cause of death,determination of the causes of injury,and identification of the foreign substances of bodies,there are only a few studies on the estimation of time of death.We detected the process of subtle changes in adult rabbits after death,the shape and size of tissues and organs,and the relationship between adjacent organs in three-dimensional space in an efiort to develop new method for the estimation of PMI.The bodies of the dead rabbits were stored at 20℃ room temperature,sealed condition,and prevented exposure to flesh flies.The dead rabbits were randomly divided into comparison group and experimental group.The whole-body CT scans were performed on the experimental group of rabbits at different PMIs.NeuViz dual-slice spiral CT scanner(made by Neusoft Medical in China,2 mm×10 mm high-speed rare earth ceramic detector)is a 360°scan that could obtain two images,capable of providing a wide range of high-speed continuous spiral scan.Max Viewer(Version:1.0.0131,Neusoft,Shenyang,China)is a CT image viewing software developed by Neusoft Medical.The software can be used to view and process images in various common methods and to measure a number of parameters,such as length,area,angle,and CT values.Statistical analysis was performed using SPSS1 Statistics 19.0(SPSS,Inc.,Chicago,IL,USA).AP<0.05 was considered statistically significant.We obtained the binomial regression equation of the CT values and the related coefficient(R^(2)).In the future,we suggests that comprehensive analyses of various indicators of different organs could establish a diversified pattern to remedy the deficiencies and make the study of PMI estimation more scientific and enhance the operability.

Computational Complexity of a Solution for Directed Graph Cooperative Games

Abstrac Khmelnitskaya et al.have recently proposed the average covering tree value as a new solution concept for cooperative transferable utility games with directed graph structure.The average covering tree value is defined as the average of marginal contribution vectors corresponding to the specific set of rooted trees,and coincides with the Shapley value when the game has complete communication structure.In this paper,we discuss the computational complexity of the average covering tree value.We show that computation of the average covering tree value is#P-complete even if the characteristic function of the game is{0,1}-valued.We prove this by a reduction from counting the number of all linear extensions of a partial order,which has been shown by Brightwell et al.to be a#P-complete counting problem.The implication of this result is that an efficient algorithm to calculate the average covering tree value is unlikely to exist.