Dispersion Relations in Diffraction in Time

In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, g(x′)=±Sgn(x′)g(x′), which defines the property of being a truncated functions at the origin. On the other hand, we prove that the wave-function of a generalized diffraction in time problem is just the Fourier-transform of a truncated function. Consequently, the existence of dispersion relations for the diffraction in time wave-function follows. We derive these explicit dispersion relations.

Advancements in Time Modeling: Relationalism, Divisional Structures, and Geometry

This article broadens terminology and approaches that continue to advance time modelling within a relationalist framework. Time is modeled as a single dimension, flowing continuously through independent privileged points. Introduced as absolute point-time, abstract continuous time is a backdrop for concrete relational-based time that is finite and discrete, bound to the limits of a real-world system. We discuss how discrete signals at a point are used to temporally anchor zero-temporal points [t = 0] in linear time. Object-oriented temporal line elements, flanked by temporal point elements, have a proportional geometric identity quantifiable by a standard unit system and can be mapped on a natural number line. Durations, line elements, are divisible into ordered unit ratio elements using ancient timekeeping formulas. The divisional structure provides temporal classes for rotational (Rt24t) and orbital (Rt18) sample periods, as well as a more general temporal class (Rt12) applicable to either sample or frame periods. We introduce notation for additive cyclic counts of sample periods, including divisional units, for calendar-like formatting. For system modeling, unit structures with dihedral symmetry, group order, and numerical order are shown to be applicable to Euclidean modelling. We introduce new functions for bijective and non-bijective mapping, modular arithmetic for cyclic-based time counts, and a novel formula relating to a subgroup of Pythagorean triples, preserving dihedral n-polygon symmetries. This article presents a new approach to model time in a relationalistic framework.

Time series analysis of correlativity between pulmonary tuberculosis and seasonal meteorological factors based on theory of Human-Environmental Inter Relation

Objective:This paper aims to study the correlativity between the number of pulmonary tuberculosis (PTB) cases and seasonal meteorological factors in Beijing.Methods:Based on theory of Human-Environmental Inter Relation in Huangdi's Internal Classics,we adopted monthly cases of PTB in Beijing from 2004 to 2011,and established a Seasonal Autoregressive Integrated Moving Average (SARIMA) model.Using the cross-correlation function (CCF),we then analyzed the correlation between meteorological factors and number of infected patients.The related meteorological factors were subsequently integrated,to establish a Seasonal Autoregressive Integrated Moving Average with explanatory variables (SARIMAX) model,which was used to estimate and verify the number of PTB cases in 2012.Results:In this study,a SARIMA(0,1,1) (0,1,1)12 model was established;CCF analysis was used to reveal the correlativity between PTB and precipitation with 1 lag,relative humidity with 1 lag.Then,integrated with relative humidity with 1 lag (β =2.405,95% confidence interval:0.433-4.377),the SARIMAX prediction model was proved to be an accurate approach for predicting local situations of PTB occurrence.Conclusions:The occurrence of PTB is correlated with seasonal meteorological factors.Combining these factors,an exact prediction model can be established,to estimate of the number of PTB infected patients.

Grey interpolation approach for small time-lag samples based on grey dynamic relation analysis

Given a non-equidistant sequence or an equidistant series with one or more outliers, a grey interpolation approach considering the time lags is established for producing the missing data or correcting the abnormal values. To accomplish this, a new grey incidence model, called the grey dynamic incidence model GDIM(t), is constructed for determining whether the factors are effective to the known factor and what the time lag is between a useful factor and the specified sequence. Based on the results of the GDIM(t) model, two programming problems are designed to obtain the upper and lower bounds of the unknown or abnormal values which are regarded as grey numbers. The solutions based on the particle swarm optimization(PSO) for the nonlinear programming problems are given. To explain how it can be used in practice, this new grey interpolation approach is applied to correct an abnormal value in the sequence of an agriculture environment problem.

Quantitative structure retention relationship studies for predicting relative retention times of chlorinated phenols on gas chromatography

A new method of quantitative structure retention relationship(QSRR) studies was reported for predicting gas chromatography(GC) relative retention times(RRTs) of chlorinated phenols (CPs) using a DB 5 column. Chemical descriptors were calculated from the molecular structure of CPs and related to their gas chromatographic RRTs by using multiple linear regression analysis. The proposed model had a multiple square correlation coefficient R 2=0.970, standard error SE =0.0472, and significant level P =0.0000. The QSRR model also reveals that the gas chromatographic relative retention times of CPs are associated with physicochemical property interactions with the stationary phase,and influenced by the number of chlorine and oxygen in the CP melecules.

Cross-Correlation of Station-to-Station Free Surface Elevation Time Series for Breaking Water Waves

Free surface elevation time series of breaking water waves were measured in a laboratory flume. This was done in order to analyze changes in wave characteristics as the waves propagated from deep water to the shore. A pair of parallel- wire capacitive wave gages was used to simultaneously measure free surface elevations at different positions along the flume. One gage was kept fixed near the wave generator to provide a reference while the other was moved in steps of 0.1 m in the vicinity of the break point. Data from these two wave gages measured at the same time constitute station-to-station free surface elevation time series. Fast Fourier Transform (FFT) based cross-correlation techniques were employed to determine the time lag between each pair of the time series. The time lag was used to compute the phase shift between the reference wave gage and that at various points along the flume. Phase differences between two points spaced 0.1 m apart were used to calculate local mean wave phase velocity for a point that lies in the middle. Results show that moving from deep water to shallow water, the measured mean phase velocity decreases almost linearly from about 1.75 m/s to about 1.50 m/s at the break point. Just after the break point, wave phase velocity abruptly increases to a maximum value of 1.87 m/s observed at a position 30 cm downstream of the break point. Thereafter, the phase velocity decreases, reaching a minimum of about 1.30 m/s.

Gravitational Space-Time Quantization for Charged Wormholes and the Diophantine Uncertainty Relation

This research work proceeds from the assumption, which was still considered by Einstein, that the quantization of gravity does not require additional external procedures: quantum phenomena can be a consequence of the properties of the universal gravitational interaction, which maps any physical field upon the space-time geometry. Therefore, an attempt is made in this research work to reduce the quantization of physical fields in GRT to the space-time quantization. Three reasons for quantum phenomena are considered: Partition of space-time into a set of unconnected Novikov’s R- and T-domains impenetrable for light paths;the set is generated by the invariance of Einstein’s equations with respect to dual mappings;The existence of electric charge quanta of wormholes, which geometrically describe elementary particles in GRT. This gives rise to a discrete spectrum of their physical and geometric parameters governed by Diophantine equations. It is shown that the fundamental constants (electric charge, rest masses of an electron and a proton) are interconnected arithmetically;The existence of the so-called Diophantine catastrophe, when fluctuations in the values of physical constants tending to zero lead to fluctuations in the number of electric charges and the number of nucleons at the wormhole throats, which tend to infinity, so that the product of the increments of these numbers by the increment of physical constants forms a relation equivalent to the uncertainty relation in quantum mechanics. This suggests that space-time cannot but fluctuate, and, moreover, its fluctuations are bounded from below, so that all processes become chaotic, and the observables become averaged over this chaos.

Relation Matrix of Water Exchange for Sea Bays and Its Application

Water exchange is an important hydrodynamic character of sea bays, and it is the basis for the study of the environmental capacity of sea bays. In this paper, a relation matrix is set up to describe the interaction among different areas of a sea bay, and to predict the water quality of those areas. The relation matrix is calculated based on the numerical results from a water quality model. This method is applied to the study of water exchange and the prediction of water quality of the Bohai Sea. The Bohai Sea is divided into five areas, and the effect of seasonal wind is taken into consideration. The results show a） the relation matrix can be used to study the water exchange among different areas and predict water quality of different areas at the respective characteristic time, b） the reduction of pollutant is dependent on both water exchange and initial distribution of the pollutant, and c） the half-life time of the pollutant is longer than the half-exchange time of the sea water.

Biliary tract injury caused by different relative warm ischemia time in liver transplantation in rats

BACKGROUND: There is a controversy over the degree of liver and biliary injury caused by the period of secondary warm ischemia. A liver autotransplantation model was adopted because it excludes the effects of infection and immunological rejection on bile duct injury. This study was undertaken to assess biliary tract injury caused by relative warm ischemia (secondary warm ischemia time in the biliary tract) and reperfusion. METHODS: One hundred and two rats were randomly divided into 5 groups: group I (control); groups 11 to V, relative warm ischemia times of 0 minute, 30 minutes, I hour and 2 hours. In addition to the levels of serum alkaline phosphatase, and total bilirubin, pathomorphology assessment and TUNEL assay were performed to evaluate biliary tract damage. RESULTS: Under the conditions that there were no significant differences in warm ischemia time, cold perfusion time and anhepatic phase, group comparisons showed statistically significant differences. The least injury occurred in group H (portal vein and hepatic artery reperfused simultaneously) but the most severe injury occurred in group V (biliary tract relative warm ischemia time 2 hours). CONCLUSIONS: Relative warm ischemia is one of the factors that result in bile duct injury, and the relationship between relative warm ischemia time the bile injury degree is time-dependent. Simultaneous arterial and portal reperfusion is the best choice to avoid the bile duct injury caused by relative warm ischemia. (Hepatobiliary Pancreat Dis Int 2009; 8: 247-254)

A QSRR Study on the Relative Retention Time of Halogenated Methyl-phenyl Ethers

Halogenated methyl-phenyl ethers （anisoles） are ubiquitous organic compounds in the environment. In the present study, geometrical optimization and electrostatic potential calculations have been performed for 42 halogenated anisoles at the HF/6-31 G^＊ level. A number of statistically based parameters have been obtained. By multiple regression method, linear relationships between the gas-chromatographic relative retention time （RRT） and structural descriptors have been established for the training set of 32 halogenated anisoles. The result showed that the parameters derived from electrostatic potentials （ESPs） together with the molecular volume （Vmc） could be well used to express the quantitative structure-RRT relationships of halogenated anisoles. The best two-variable regression model gives a correlation coefficient of 0.980 and a standard deviation of 0.07, and the leave-one-out cross-validated correlation coefficient is 0.975. The goodness of the model has been further validated through exploring the predictive power for the testing set of 10 halogenated anisoles.

A Simple Method for Source Depth Estimation with Multi-path Time Delay in Deep Ocean

A method of source depth estimation based on the multi-path time delay difference is proposed. When the minimum time arrivals in all receiver depths are snapped to a certain time on time delay-depth plane, time delay arrivals of surface-bottom reflection and bottom-surface reflection intersect at the source depth. Two hydrophones deployed vertically with a certain interval are required at least. If the receiver depths are known, the pair of time delays can be used to estimate the source depth. With the proposed method the source depth can be estimated successfully in a moderate range in the deep ocean without complicated matched-field calculations in the simulations and experiments.

Investigating the Effect of Relative Width on Momentum Transfer between Main Channel and Floodplain in Rough Rectangular Compound Channel Sunder Varius Relative Depth Condition

Compound section is referred to a section the surface of which is made of several sub-sections with different flow characteristics. The difference in the hydraulic and geometry characteristics causes a complexity in flow hydraulic and creates an interaction between the main channel and floodplains, resulting in an apparent shear stress and a transverse momentum transfer. The amount of such a stress plays an important role in many river engineering measures [1]. Due to the flow complexity, the common approximate analytical methods are not enough to identify the flow profile. The FLOW3D Software with its great features in three-dimensional analysis of flow field is used as a tool to investigate the shear stress in a direct symmetrical compound rectangular channel. After the simulation of models, it is found that an increase in the relative width and relative depth parameters decreases the percentage of apparent shear stress and an increase in the relative roughness causes it to be increased [2].

Hopf bifurcation control for a coupled nonlinear relative rotation system with time-delay feedbacks

This paper investigates the Hopf bifurcations resulting from time delay in a coupled relative-rotation system with time- delay feedbacks. Firstly, considering external excitation, the dynamical equation of relative rotation nonlinear dynamical system with primary resonance and 1：1 internal resonance under time-delay feedbacks is deduced. Secondly, the averaging equation is obtained by the multiple scales method. The periodic solution in a closed form is presented by a perturbation approach. At last, numerical simulations confirm that time-delay theoretical analyses have influence on the Hopf bifurcation point and the stability of periodic solution.

Time Related Influence of α-Mercapto-β-(2-Furyl) Acrylic Acid (MFA) in Cadmium Toxicity

The effect of a-mercapto-β-(2-furyl) acrylic acid (MFA, 200 mg/kg, oral) administered 30 min or 24 h post cadmium (1 mg/kg, i.p.) exposure on cadmium toxicity, was investigated in rats. The Cd induced hepatic metallothionein was reduced by MFA treatment parallel to the depletion of hepatic Cd. However, in renal tissue,MFA caused only redistribution of metal from the paniculate to the soluble fraction. Hepatic and renal Zn and renal Cu were significantly increased on Cd exposure. MFA therapy, however, lowered the hepatic Zn and increased the renal Cu levels. The action of MFA appears to be via metal chelation rather than by MT induction.

Predicting the Relative Retention Time (RRT) of Polybrominated Diphenyl Ethers (PBDEs)

Using the molecular electronegativity distance vector descriptors derived directly from the molecular topological structures, the relative retention time （RRT） of polybrominated diphenyl ethers （PBDEs） were predicted. A four-variable regression model （M30） with the correlation coefficient of 0.9816 and the root mean square errors of 0.061 was developed using a training set including 30 PBDEs. The correlation coefficient of 0.9841 and the root mean square errors of 0.054 between the values of RRT predicted by M30 and the RRT observed for 16 external PBDEs show a good predictive potential of M30. The descriptors included in the M30 represent four interactions between four pairs of atom types, i.e., atom -C= and -C=, -C= and 〉C=, 〉C= and 〉C=, -C= and -Br.

The determination of the relative permittivity of periodic stratified media based on the iterative time-reversal method

In this paper, we present a new method to determine the relative permittivity of periodic stratified media using the iterative time-reversal method. Based on transmission line theory, the focal peak value of iterative time-reversal electro- magnetic waves, which contain information about the periodic stratified medium, is computed in pulse-echo mode. Using the relationship between the focal peak value and the relative permittivity of the periodic stratified medium, the relative permittivity can be obtained by measuring the focal peak value. Numerical simulations are conducted, and the results demonstrate the feasibility of the proposed approach to the measurement of the relative permittivity of a periodic stratified medium.

Fast Evaluation of Time-Domain Green Function for Finite Water Depth

For computation of large amplitude motions of ships fastened to a dock, a fast evaluation scheme is implemented for computation of the time-domain Green function for finite water depth. Based on accurate evaluation of the Green function directly, a fast approximation method for the Green function is developed by use of Chebyshev polynomials. Examinations are carried out of the accuracy of the Green function and its derivatives from the scheme. It is shown that when an appropriate number of polynomial terms are used, very accurate approximation can be obtained.

Extension of Subjective Logic for Time-Related Trust

To describe the dynamic propcrty of trust relationship, wt propose atime-related trust model and extend Joang's subjective logic to fit for time-related trust model.The extension includes prepositional conjunction, disjunction and negation for traditional logic anddiscounting and consensus operators that are evidential operators specially designed for thepropagation and computation of trust relationships. With the extension of subjective logic fortime-related trust, our time-related trust modelis suitable to model the dynamic trust relationshipin practice. Finally an example of reputation assessment is offered to demonstrate the usage of ourtrust model.

Traveltime tomography and prestack depth migration for vertical seismic profiling of an angle-domain walkaway on a complex surface

Walkaway VSP cannot obtain accurate velocity field,as it asymmetrically reflects ray path and provides uneven coverage to underground target,thereby presenting issues related to imaging quality.In this study,we propose combining traveltime tomography and prestack depth migration for VSP of an angle-domain walkaway,in a bid to establish accurate two-dimensional and three-dimensional(3 D)velocity models.First,residual curvature was defined to update velocity,and an accurate velocity field was established.To establish a high-precision velocity model,we deduced the relationship between the residual depth and traveltime of common imaging gathers(CIGs)in walkaway VSP.Solving renewal velocity using the least squares method,a four-parameter tomographic inversion equation was derived comprising formation dip angle,incidence angle,residual depth,and sensitivity matrix.In the angle domain,the reflected wave was divided into up-and down-transmitted waves and their traveltimes were calculated.The systematic cumulative method was employed in prestack depth migration of a complex surface.Through prestack depth migration,the offset-domain CIGs were obtained,and dip angle was established by defining the stack section horizon.Runge–Kutta ray tracing was employed to calculate the ray path from the reflection point to the detection point,to determine the incident angle,and to subsequently calculate the ray path from the reflection point to the irregular surface.The offset-domain residual depths were mapped to the angle domain,and a new tomographic equation was established and solved.Application in the double complex area of the Tarim Basin showed the four-parameter tomographic inversion equation derived in this paper to be both correct and practical and that the migration algorithm was able to adapt to the complex surface.

Comparison of time-related electrical properties of PN junctions and Schottky diodes for Zn O-based betavoltaic batteries

Schottky diodes and PN junctions were utilized as energy converting structures in ZnO-based betavoltaic batteries,in which 0.101121 Ci 63Ni was selected as the beta source.The time-related electrical properties were obtained using Monte Carlo simulations.For the n-type ZnO,the Pt/ZnO Schottky diode had the highest energy conversion efficiency,and the Ni/ZnO Schottky diode had the largest Isc.The overall electrical performance of PN junctions is better than that of Schottky diodes.The lifetimes of Pt/ZnO and Ni/ZnO are longer than for other Schottky devices,coming close to those of PN junctions.Considering that Schottky diodes are easier to fabricate and independent of p-type semiconductors,Pt/ZnO and Ni/ZnO diodes offer alternatives to PN-junction-based betavoltaic batteries.