VALIDITY OF ONE-WAY MODELS IN THE WEAK RANGE DEPENDENCE LIMIT

2004 ◽  
Vol 12 (01) ◽  
pp. 55-66 ◽  
Author(s):  
JIANXIN ZHU ◽  
YA YAN LU
Keyword(s):  
Helmholtz Equation ◽  
Numerical Solutions ◽  
Underwater Acoustics ◽  
Square Root ◽  
Orthogonal Transform ◽  
The Difference ◽  
The One ◽  
Dirichlet To Neumann Map ◽  
Root Operator ◽  
Marching Method

Numerical solutions of the Helmholtz equation and the one-way Helmholtz equation are compared in the weak range dependence limit, where the overall range distance is increased while the range dependence is weakened. It is observed that the difference between the solutions of these two equations persists in this limit. The one-way Helmholtz equation involves a square root operator and it can be further approximated by various one-way models used in underwater acoustics. An operator marching method based on the Dirichlet-to-Neumann map and a local orthogonal transform is used to solve the Helmholtz equation.

scholarly journals Reliable Change Formula Query: Temkin et al. reply

2000 ◽  
Vol 6 (3) ◽  
pp. 364-364 ◽  
Author(s):  
NANCY R. TEMKIN ◽  
ROBERT K. HEATON ◽  
IGOR GRANT ◽  
SUREYYA S. DIKMEN
Keyword(s):  
Standard Deviation ◽  
Standard Error ◽  
Direct Method ◽  
Single Point ◽  
Reliability Coefficient ◽  
Reliable Change Index ◽  
Square Root ◽  
Reliable Change ◽  
The Difference ◽  
The One

Hinton-Bayre (2000) raises a point that may occur to many readers who are familiar with the Reliable Change Index (RCI). In our previous paper comparing four models for detecting significant change in neuropsychological performance (Temkin et al., 1999), we used a formula for calculating Sdiff, the measure of variability for the test–retest difference, that differs from the one Hinton-Bayre has seen employed in other studies of the RCI. In fact, there are two ways of calculating Sdiff—a direct method and an approximate method. As stated by Jacobson and Truax (1991, p. 14), the direct method is to compute “the standard error of the difference between the two test scores” or equivalently [begin square root](s12 + s22 − 2s1s2rxx′)[end square root] where si is the standard deviation at time i and rxx′ is the test–retest correlation or reliability coefficient. Jacobson and Truax also provide a formula for the approximation of Sdiff when one does not have access to retest data on the population of interest, but does have a test–retest reliability coefficient and an estimate of the cross-sectional standard deviation, i.e., the standard deviation at a single point in time. This approximation assumes that the standard deviations at Time 1 and Time 2 are equal, which may be close to true in many cases. Since we had the longitudinal data to directly calculate the standard error of the difference between scores at Time 1 and Time 2, we used the direct method. Which method is preferable? When the needed data are available, it is the one we used.

scholarly journals The effects of the model errors generated by discretization of "on-off'' processes on VDA

2006 ◽  
Vol 13 (3) ◽  
pp. 309-320 ◽  
Author(s):  
Q. Zheng ◽  
M. Mu
Keyword(s):  
Governing Equation ◽  
Numerical Solutions ◽  
Model Error ◽  
Forward Model ◽  
Threshold Condition ◽  
Model Errors ◽  
The Difference ◽  
The One ◽  
Adjoint Approach ◽  
Theoretical Analyses

Abstract. Through an idealized model of a partial differential equation with discontinuous "on-off'' switches in the forcing term, we investigate the effect of the model error generated by the traditional discretization of discontinuous physical "on-off'' processes on the variational data assimilation (VDA) in detail. Meanwhile, the validity of the adjoint approach in the VDA with "on-off'' switches is also examined. The theoretical analyses illustrate that in the analytic case, the gradient of the associated cost function (CF) with respect to an initial condition (IC) exists provided that the IC does not trigger the threshold condition. But in the discrete case, if the on switches (or off switches) in the forward model are straightforwardly assigned the nearest time level after the threshold condition is (or is not) exceeded as the usual treatment, the discrete CF gradients (even the one-sided gradient of CF) with respect to some ICs do not exist due to the model error, which is the difference between the analytic and numerical solutions to the governing equation. Besides, the solution of the corresponding tangent linear model (TLM) obtained by the conventional approach would not be a good first-order linear approximation to the nonlinear perturbation solution of the governing equation. Consequently, the validity of the adjoint approach in VDA with parameterized physical processes could not be guaranteed. Identical twin numerical experiments are conducted to illustrate the influences of these problems on VDA when using adjoint method. The results show that the VDA outcome is quite sensitive to the first guess of the IC, and the minimization processes in the optimization algorithm often fail to converge and poor optimization retrievals would be generated as well. Furthermore, the intermediate interpolation treatment at the switch times of the forward model, which reduces greatly the model error brought by the traditional discretization of "on-off'' processes, is employed in this study to demonstrate that when the "on-off'' switches in governing equations are properly numerically treated, the validity of the adjoint approach in VDA with discontinuous physical "on-off'' processes can still be guaranteed.

Finite‐difference migration derived from the Kirchhoff‐Helmholtz integral

Geophysics ◽  
1996 ◽  
Vol 61 (5) ◽  
pp. 1394-1399 ◽  
Author(s):  
Thomas Rühl
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Continued Fraction ◽  
Velocity Fields ◽  
Finite Difference Schemes ◽  
Square Root ◽  
Continued Fraction Expansion ◽  
The One ◽  
Root Operator ◽  
Approximate Version

Finite‐difference (FD) migration is one of the most often used standard migration methods in practice. The merit of FD migration is its ability to handle arbitrary laterally and vertically varying macro velocity fields. The well‐known disadvantage is that wave propagation is only performed accurately in a more or less narrow cone around the vertical. This shortcoming originates from the fact that the exact one‐way wave equation can be implemented only approximately in finite‐difference schemes because of economical reasons. The Taylor or continued fraction expansion of the square root operator in the one‐way wave equation must be truncated resulting in an approximate version of the one‐way wave equation valid only for a restricted angle range.

Use of a Lyophilized Reference Plasma to Compare Coagulation Test Procedures

1975 ◽  
Vol 34 (02) ◽  
pp. 426-444 ◽  
Author(s):  
J Kahan ◽  
I Nohén
Keyword(s):  
Oral Anticoagulant Therapy ◽  
Repeated Measurements ◽  
Test Procedures ◽  
Coagulation Activity ◽  
Close Relationship ◽  
Measured Activity ◽  
Test Materials ◽  
The Difference ◽  
The Stability ◽  
The One

SummaryIn 4 collaborative trials, involving a varying number of hospital laboratories in the Stockholm area, the coagulation activity of different test materials was estimated with the one-stage prothrombin tests routinely used in the laboratories, viz. Normotest, Simplastin-A and Thrombotest. The test materials included different batches of a lyophilized reference plasma, deep-frozen specimens of diluted and undiluted normal plasmas, and fresh and deep-frozen specimens from patients on long-term oral anticoagulant therapy.Although a close relationship was found between different methods, Simplastin-A gave consistently lower values than Normotest, the difference being proportional to the estimated activity. The discrepancy was of about the same magnitude on all the test materials, and was probably due to a divergence between the manufacturers’ procedures used to set “normal percentage activity”, as well as to a varying ratio of measured activity to plasma concentration. The extent of discrepancy may vary with the batch-to-batch variation of thromboplastin reagents.The close agreement between results obtained on different test materials suggests that the investigated reference plasma could be used to calibrate the examined thromboplastin reagents, and to compare the degree of hypocoagulability estimated by the examined PIVKA-insensitive thromboplastin reagents.The assigned coagulation activity of different batches of the reference plasma agreed closely with experimentally obtained values. The stability of supplied batches was satisfactory as judged from the reproducibility of repeated measurements. The variability of test procedures was approximately the same on different test materials.

The Demand For Money in Pakistan: Reply (Notes and Comments)

1975 ◽  
Vol 14 (3) ◽  
pp. 370-375
Author(s):  
M. A. Akhtar
Keyword(s):  
Interest Rates ◽  
Money Demand ◽  
Strong Support ◽  
Physical Capital ◽  
Careful Examination ◽  
Demand For Money ◽  
Weak Support ◽  
Complementarity Hypothesis ◽  
The Difference ◽  
The One

I am grateful to Abe, Fry, Min, Vongvipanond, and Yu (hereafter re¬ferred to as AFMVY) [1] for obliging me to reconsider my article [2] on the demand for money in Pakistan. Upon careful examination, I find that the AFMVY results are, in parts, misleading and that, on the whole, they add very little to those provided in my study. Nevertheless, the present exercise as well as the one by AFMVY is useful in that it furnishes us with an opportunity to view some of the fundamental problems involved in an empi¬rical analysis of the demand for money function in Pakistan. Based on their elaborate critique, AFMVY reformulate the two hypo¬theses—the substitution hypothesis and the complementarity hypothesis— underlying my study and provide us with some alternative estimates of the demand for money in Pakistan. Briefly their results, like those in my study, indicate that income and interest rates are important in deter¬mining the demand for money. However, unlike my results, they also suggest that the price variable is a highly significant determinant of the money demand function. Furthermore, while I found only a weak support for the complementarity between money demand and physical capital, the results obtained by AFMVY appear to yield a strong support for that rela¬tionship.1 The difference in results is only a natural consequence of alter¬native specifications of the theory and, therefore, I propose to devote most of this reply to the criticisms raised by AFMVY and the resulting reformulation of the two mypotheses.

Effect of leakage and blockage on the acoustic behavior of particle filters

2019 ◽  
Vol 67 (6) ◽  
pp. 483-492
Author(s):  
Seonghyeon Baek ◽  
Iljae Lee
Keyword(s):  
Transfer Matrix ◽  
Particle Filters ◽  
Acoustic Analysis ◽  
Transmission Loss ◽  
One Dimensional ◽  
Filter System ◽  
The Difference ◽  
The One ◽  
Analytical Approaches ◽  
Good Agreement

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.

Development and Validation of Spectrophotometric and Liquid Chromatographic Methods for Estimation of Tigecycline in Injections

2020 ◽  
Vol 13 (5) ◽  
pp. 5148-5154
Author(s):  
Sagar Suman Panda ◽  
Ravi Kumar B.V.V.
Keyword(s):  
Area Under The Curve ◽  
Reversed Phase ◽  
Equal Concentration ◽  
Pharmaceutical Dosage Form ◽  
Liquid Chromatographic Method ◽  
Array Detection ◽  
The Difference ◽  
The One ◽  
Development And Validation ◽  
Liquid Chromatographic

Three new analytical methods were optimized and validated for the estimation of tigecycline (TGN) in its injection formulation. A difference UV spectroscopic, an area under the curve (AUC), and an ultrafast liquid chromatographic (UFLC) method were optimized for this purpose. The difference spectrophotometric method relied on the measurement of amplitude when equal concentration solutions of TGN in HCl are scanned against TGN in NaOH as reference. The measurements were done at 340 nm (maxima) and 410nm (minima). Further, the AUC under both the maxima and minima were measured at 335-345nm and 405-415nm, respectively. The liquid chromatographic method utilized a reversed-phase column (150mm×4.6mm, 5µm) with a mobile phase of methanol: 0.01M KH2PO4 buffer pH 3.5 (using orthophosphoric acid) in the ratio 80:20 %, v/v. The flow rate was 1.0ml/min, and diode array detection was done at 349nm. TGN eluted at 1.656min. All the methods were validated for linearity, precision, accuracy, stability, and robustness. The developed methods produced validation results within the satisfactory limits of ICH guidance. Further, these methods were applied to estimate the amount of TGN present in commercial lyophilized injection formulations, and the results were compared using the One-Way ANOVA test. Overall, the methods are rapid, simple, and reliable for routine quality control of TGN in the bulk and pharmaceutical dosage form. 

Managing the Era of Multi-Cultural Leadership

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
M. Rahul ◽  
R. Ganesan
Keyword(s):  
Work Environment ◽  
Leadership Style ◽  
Work Experience ◽  
Cross Culture ◽  
Cultural Leadership ◽  
Team Members ◽  
Diverse Workforce ◽  
The Difference ◽  
The One ◽  
Global Arena

Leaders in the global arena are the one who face the challenges never seen before, while coordinating work and managing relationship between team members coming from varied ethnic groups. Globalization has undoubtedly opened up endless growth opportunities for both, businesses and individuals, by collaborating with each other, but with certain inherent challenges. These challenges are the difference in the cultural background of the team members, which gets predominantly reflected in their behavior at workplace too. The cultural differences exist primarily due to differences in shared values, which form the basis for difference in perception and practices of decision making by an individual (Hofstede, 1980). Juana Bordas has rightly described that any business that fails to adapt their leadership style aligning with multi-cultural approach will find it difficult to thrive in a more colorful world. Leadership style has witnessed various facets of changing work environment that has demanded from leaders to modify their approach to adapt along and be effective and survive in the ever-changing environment of business (Bordas,2007).A cross-culture leader plays a significant role in knitting the diverse workforce into an efficient team; which requires a leader to very well understand the various dimensions of culture. This understanding of the leader enables him to learn about blending of leadership styles to address the challenges of such work environment. This paper is an extended work on 'Leadership in Cross-Cultural Environment – A Comparison of Asian and Non-Asian Managers' (Rahul and Ganesan, 2015). The extended research study has identified that enhanced work experience of cross-culture leaders enables them in effective team management, than the rise in designation, as it results in creation of hierarchical distance between the leaders and subordinates.

Defending the Difference

2017 ◽  
Keyword(s):  
Social Sciences ◽  
Natural Sciences ◽  
Point Of View ◽  
True Nature ◽  
Natural Entities ◽  
The Social ◽  
The World ◽  
Methodological Difference ◽  
The Difference ◽  
The One

Dreyfus argues that there is a basic methodological difference between the natural sciences and the social sciences, a difference that derives from the different goals and practices of each. He goes on to argue that being a realist about natural entities is compatible with pluralism or, as he calls it, “plural realism.” If intelligibility is always grounded in our practices, Dreyfus points out, then there is no point of view from which one can ask about or provide an answer to the one true nature of ultimate reality. But that is consistent with believing that the natural sciences can still reveal the way the world is independent of our theories and practices.

scholarly journals Plastic failure zone characteristics and stability control technology of roadway in the fault area under non-uniformly high geostress: A case study from Yuandian Coal Mine in Northern Anhui Province, China

2020 ◽  
Vol 12 (1) ◽  
pp. 406-424 ◽  
Author(s):  
Yaoguang Huang ◽  
Aining Zhao ◽  
Tianjun Zhang ◽  
Weibin Guo
Keyword(s):  
Numerical Methods ◽  
Numerical Solutions ◽  
Stress Test ◽  
Pressure Coefficient ◽  
Stability Control ◽  
Failure Zone ◽  
Plastic Failure ◽  
Comparison Results ◽  
High Geostress ◽  
The Difference

AbstractIn order to explore the effective support method for deep broken roadway, based on the in situ stress test results, the analytical and numerical solutions of the stress and the range of plastic failure zone (PFZ) in a circular roadway subjected to non-uniform loads were obtained using analytical and finite difference numerical methods based on the elastoplastic theory, respectively. Their comparison results show that the analytical and numerical methods are correct and reasonable. Furthermore, the high geostress causes the stress and range of PFZ in roadway roof and floor to increase sharply while those in roadway ribs decrease. Moreover, the greater the difference of horizontal geostress in different horizontal directions is, the larger the range of PFZ in roadway roof and floor is. The shape of PFZ in roadway varies with the ratio of horizontal lateral pressure coefficient in x-direction and y-direction. Finally, according to the distribution characteristics of PFZ and range of PFZ under the non-uniformly high geostress, this paper has proposed a combined support scheme, and refined and optimized supporting parameters. The field monitoring results prove that the roadway deformation and fracture have been effectively controlled. The research results of this paper can provide theoretical foundation as well as technical reference for the stability control of deep broken roadway under non-uniformly high geostress.

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