scholarly journals Caustic Frequency in 2D Stochastic Flows Modeling Turbulence

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 797
Author(s):  
Leonid I. Piterbarg
Keyword(s):  
Stokes Number ◽  
Upper And Lower Bounds ◽  
Stochastic Flows ◽  
Uniqueness Of Solutions ◽  
Stochastic Forcing ◽  
Nonlinear Stochastic Differential Equations ◽  
Special Cases ◽  
The Mean ◽  
The One ◽  
Mean Time

Stochastic flows mimicking 2D turbulence in compressible media are considered. Particles driven by such flows can collide and we study the collision (caustic) frequency. Caustics occur when the Jacobian of a flow vanishes. First, a system of nonlinear stochastic differential equations involving the Jacobian is derived and reduced to a smaller number of unknowns. Then, for special cases of the stochastic forcing, upper and lower bounds are found for the mean number of caustics as a function of Stokes number. The bounds yield an exact asymptotic for small Stokes numbers. The efficiency of the bounds is verified numerically. As auxiliary results we give rigorous proofs of the well known expressions for the caustic frequency and Lyapunov exponent in the one-dimensional model. Our findings may also be used for estimating the mean time when a 2D Riemann type partial differential equation with a stochastic forcing loses uniqueness of solutions.

scholarly journals Steady states of the reaction-diffusion equations. Part II: Uniqueness of solutions and some special cases

1983 ◽  
Vol 24 (4) ◽  
pp. 392-416 ◽  
Author(s):  
J. G. Burnell ◽  
A. A. Lacey ◽  
G. C. Wake
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Uniqueness Of Solutions ◽  
One Dimensional ◽  
Nonlinear Elliptic ◽  
Special Cases ◽  
Exothermic Chemical Reaction ◽  
Dimensional Shape ◽  
The One ◽  
Special Case

AbstractIn an earlier paper (Part I) the existence and some related properties of the solution to a coupled pair of nonlinear elliptic partial differential equations was considered. These equations arise when material is undergoing an exothermic chemical reaction which is sustained by the diffusion of a reactant. In this paper we consider the range of parameters for which the uniqueness of solution is assured and we also investigate the converse question of multiple solutions. The special case of the one dimensional shape of the infinite slab is investigated in full as this case admits to solution by integration.

scholarly journals Evaluation of Time Consumption for Debonding Brackets Using Different Techniques: A Hospital-Based Study

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Neelutpal Bora ◽  
Putul Mahanta ◽  
Ranjumoni Konwar ◽  
Bharati Basumatari ◽  
Chiranjita Phukan ◽  
...  
Keyword(s):  
Time Range ◽  
Thermal Method ◽  
Anova Test ◽  
Time Consumption ◽  
The Mean ◽  
The Difference ◽  
The One ◽  
Time Required ◽  
Mean Time ◽  
One Way Anova

Background and Objectives. The debonding procedures of brackets in orthodontics cause a different amount of time loss and enamel damage. The current research assesses and equates the time consumption for bracket debonding using four different techniques. Materials and Methods. A total of 80 human premolars were included in this study. The samples were first arranged following a standard protocol for bracketing and then debonded using the ultrasonic scaler (US), debonding plier (DP), ligature cutter (LC), and thermal method (TM). Depending on the technique applied for debonding, the specimens were randomly divided into four groups with 20 samples, each keeping a 1 : 1 ratio. During the debonding process, the time taken for each bracket removal was recorded using a stopwatch. To assess the difference in mean time required for debonding among the four techniques, one-way ANOVA test was applied along with Tukey’s HSD to compare the two methods. Results. The time range and the mean time required for the four techniques analyzed show that the DP method has the highest range of time needed for debonding with 0.97–2.56 seconds, while LC methods have the least time range taking 0.46 to 1.79 seconds. TM’s mean time to debond is the highest at 1.5880 seconds. LC method has the lowest mean debonding time of 0.9880 seconds. The one-way ANOVA test has shown the mean debonding time required by the four techniques to be significantly different ( p < 0.001 ). Tukey’s HSD multiple comparisons also show that the mean time to debond using the LC method is substantially less than the other three methods ( p < 0.001 ). Conclusion. The mean debonding time for the TM was substantially the highest, followed by the US and DP. Debonding with the LC technique required the least time. This study shows some limelight towards the effectiveness of the LC method as it is the least time-consuming technique.

Survival probabilities and extinction times for some multitype branching processes

1974 ◽  
Vol 6 (03) ◽  
pp. 446-462 ◽  
Author(s):  
Edward Pollak
Keyword(s):  
Generating Functions ◽  
Branching Processes ◽  
Upper And Lower Bounds ◽  
Single Individual ◽  
Survival Probabilities ◽  
Time To Extinction ◽  
Special Cases ◽  
Multitype Branching Processes ◽  
Mean Time To Extinction ◽  
Mean Time

This paper deals with the computation of survival probabilities and extinction times for multitype positively regular branching processes. If all of the generating functions of the offspring distributions are of the linear fractional form and have the same denominator, explicit expressions may be obtained for all of their iterates. It is then possible to obtain formulae for survival probabilities and bounds on the mean time to extinction, given extinction, of a line descended from a single individual. If there are two types and the offspring distributions are bivariate Poisson, their generating functions may be bounded by linear fractional generating functions. It is then possible to compute upper and lower bounds on mean times to extinction, given extinction, and this is done for some special cases.

Survival probabilities and extinction times for some multitype branching processes

1974 ◽  
Vol 6 (3) ◽  
pp. 446-462 ◽  
Author(s):  
Edward Pollak
Keyword(s):  
Generating Functions ◽  
Branching Processes ◽  
Upper And Lower Bounds ◽  
Single Individual ◽  
Survival Probabilities ◽  
Time To Extinction ◽  
Special Cases ◽  
Multitype Branching Processes ◽  
Mean Time To Extinction ◽  
Mean Time

This paper deals with the computation of survival probabilities and extinction times for multitype positively regular branching processes. If all of the generating functions of the offspring distributions are of the linear fractional form and have the same denominator, explicit expressions may be obtained for all of their iterates. It is then possible to obtain formulae for survival probabilities and bounds on the mean time to extinction, given extinction, of a line descended from a single individual. If there are two types and the offspring distributions are bivariate Poisson, their generating functions may be bounded by linear fractional generating functions. It is then possible to compute upper and lower bounds on mean times to extinction, given extinction, and this is done for some special cases.

AVERAGE RUN LENGTHS FOR MOVING AVERAGE CONTROL CHARTS

1999 ◽  
Vol 13 (2) ◽  
pp. 209-220 ◽  
Author(s):  
Sheldon M. Ross
Keyword(s):  
Control Charts ◽  
Moving Average ◽  
Upper And Lower Bounds ◽  
Recursive Procedure ◽  
Efficient Simulation ◽  
Population Distributions ◽  
Average Control ◽  
The Mean ◽  
Run Lengths ◽  
Mean Time

We are interested in E [N], the mean time until the most recent k values of a sequence of independent and identically distributed random variables exceeds a specified constant. Using recent results, we present a simulation procedure for determining E [N]. These results are also used to obtain upper and lower bounds for E [N]. These bounds, however, are in terms of a quantity ω that is not easily calculated. A recursive procedure for evaluating ω when the data distribution is Bernoulli is given. Efficient simulation procedures for estimating ω in the cases of normal and exponential population distributions are also presented, as is a Markov chain monte carlo procedure when the distribution is general.

Time to Delivery after Scheduled Shirodkar Cerclage Removal in Singleton Gestations based on the Original Indication for Cerclage Placement

2018 ◽  
Vol 36 (04) ◽  
pp. 341-345
Author(s):  
Nathan Fox ◽  
Jennifer Lam-Rachlin ◽  
Simi Gupta ◽  
Mariam Naqvi ◽  
Julie Romero ◽  
...  
Keyword(s):  
Primary Outcome ◽  
Chi Square ◽  
Maternal Fetal Medicine ◽  
Gestational Age At Delivery ◽  
Chi Square Test ◽  
The Mean ◽  
The One ◽  
Time To Delivery ◽  
Mean Time ◽  
Singleton Pregnancies

Objective To estimate the time to delivery after elective cerclage removal and evaluate whether there is a difference based on the indication for cerclage placement. Study Design This was a retrospective cohort of singleton pregnancies that underwent Shirodkar cerclage placement at a single maternal–fetal medicine practice between June 2005 and June 2017. We included all scheduled elective cerclage removals >36 weeks. The primary outcome was latency to delivery. We further compared time to delivery based on the original indication for cerclage. Data were analyzed using the one-way analysis of variance and chi-square test. Results A total of 143 patients met the inclusion criteria. Of these, 40.6% were history indicated, 51.0% ultrasound indicated, and 8.4% exam indicated. The mean time from removal to delivery was 13.3 ± 8.4 days; 12.6% (18/136) of patients delivered within 24 hours of removal. When stratified by indication for cerclage, there were no significant differences for all delivery outcomes. Delaying cerclage removal to >37 weeks resulted in a statistically significantly later gestational age at delivery compared with removal between 36 and 366/7 weeks (39.0 vs. 38.3 weeks, p = 0.001). Conclusion The mean time from elective Shirodkar cerclage removal to delivery is 13 days with only 12.6% of patients delivering within 24 hours of removal.

scholarly journals Favorite-Candidate Voting for Eliminating the Least Popular Candidate in a Metric Space

2020 ◽  
Vol 34 (02) ◽  
pp. 1894-1901
Author(s):  
Xujin Chen ◽  
Minming Li ◽  
Chenhao Wang
Keyword(s):  
Lower Bounds ◽  
Metric Space ◽  
Social Value ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
The Social ◽  
Special Cases ◽  
Worst Case Ratio ◽  
The One

We study single-candidate voting embedded in a metric space, where both voters and candidates are points in the space, and the distances between voters and candidates specify the voters' preferences over candidates. In the voting, each voter is asked to submit her favorite candidate. Given the collection of favorite candidates, a mechanism for eliminating the least popular candidate finds a committee containing all candidates but the one to be eliminated. Each committee is associated with a social value that is the sum of the costs (utilities) it imposes (provides) to the voters. We design mechanisms for finding a committee to optimize the social value. We measure the quality of a mechanism by its distortion, defined as the worst-case ratio between the social value of the committee found by the mechanism and the optimal one. We establish new upper and lower bounds on the distortion of mechanisms in this single-candidate voting, for both general metrics and well-motivated special cases.

scholarly journals Assessing the probability of freedom from pine wood nematode based on 19 years of surveys

NeoBiota ◽  
2020 ◽  
Vol 58 ◽  
pp. 75-106
Author(s):  
Salla Hannunen ◽  
Juha Tuomola
Keyword(s):  
Early Detection ◽  
Quantitative Estimate ◽  
Bursaphelenchus Xylophilus ◽  
Pine Wood Nematode ◽  
Pine Wood ◽  
Quarantine Pest ◽  
System Sensitivity ◽  
The Mean ◽  
The One ◽  
Mean Time

Many quarantine pests, such as the pine wood nematode (PWN, Bursaphelenchus xylophilus), are surveyed annually in all EU countries. Although a lot of resources are spent in the surveys, the confidence in pest freedom achieved with them is not commonly analysed. We assessed the probability that Finland is free from PWN, based on the surveys done in 2000–2018. We used the methods employed in the risk-based estimate of system sensitivity tool (RiBESS), which has recently been recommended for quarantine pest applications. We considered two scenarios: 1) the surveys aimed to justify phytosanitary import requirements and to facilitate exports and 2) the surveys aimed to detect invasions early to enable eradication of outbreaks. These differed only in the pest prevalence that the surveys were expected to detect. The surveys appeared to support the assumption that PWN is not present in Finland, but they did not seem extensive enough to ensure early detection of invasions. The sensitivity of the import-export surveys was greater than 0.6 in 13 years, whereas that of the early detection surveys was always below 0.25. The probability of freedom achieved in 2018 following 19 years of surveys increased asymptotically with the mean time between invasions. For the import-export surveys, this probability was at least 0.95 unless the mean time between invasions was less than 13 years. For the early detection surveys, the probability of freedom was less than 0.73 unless the mean time between invasions was 63 years or more. The results were rather robust with respect to the parameters for which exact information was lacking. To improve the assessment, a quantitative estimate of the probability of PWN invasion to Finland and a thorough assessment of the maximum area of an eradicable infestation would be needed. To gain an understanding about the true impact of quarantine pest surveys on biosecurity, more assessments, like the one presented in this paper, are needed.

Decoration technique and surface physics

1978 ◽  
Vol 36 (1) ◽  
pp. 436-437 ◽  
Author(s):  
H. Bethge
Keyword(s):  
Diffusion Path ◽  
Special Importance ◽  
Surface Physics ◽  
Step Structure ◽  
Initial Stage ◽  
Special Cases ◽  
Atomic Surface ◽  
The Mean ◽  
Bulk Structure ◽  
Decoration Technique

Besides the atomic surface structure, diverging in special cases with respect to the bulk structure, the real structure of a surface Is determined by the step structure. Using the decoration technique /1/ it is possible to image step structures having step heights down to a single lattice plane distance electron-microscopically. For a number of problems the knowledge of the monatomic step structures is important, because numerous problems of surface physics are directly connected with processes taking place at these steps, e.g. crystal growth or evaporation, sorption and nucleatlon as initial stage of overgrowth of thin films.To demonstrate the decoration technique by means of evaporation of heavy metals Fig. 1 from our former investigations shows the monatomic step structure of an evaporated NaCI crystal. of special Importance Is the detection of the movement of steps during the growth or evaporation of a crystal. From the velocity of a step fundamental quantities for the molecular processes can be determined, e.g. the mean free diffusion path of molecules.

Predicting Daily Maintenance Dose of Fluindione, an Oral Anticoagulant Drug

1996 ◽  
Vol 75 (05) ◽  
pp. 731-733 ◽  
Author(s):  
V Cazaux ◽  
B Gauthier ◽  
A Elias ◽  
D Lefebvre ◽  
J Tredez ◽  
...  
Keyword(s):  
Effective Dose ◽  
Maintenance Dose ◽  
Successive Approximations ◽  
Hemorrhagic Complication ◽  
Simple Method ◽  
Individual Variations ◽  
Anticoagulant Drug ◽  
The Mean ◽  
Mean Time ◽  
Daily Maintenance Dose

SummaryDue to large inter-individual variations, the dose of vitamin K antagonist required to target the desired hypocoagulability is hardly predictible for a given patient, and the time needed to reach therapeutic equilibrium may be excessively long. This work reports on a simple method for predicting the daily maintenance dose of fluindione after the third intake. In a first step, 37 patients were delivered 20 mg of fluindione once a day, at 6 p.m. for 3 consecutive days. On the morning of the 4th day an INR was performed. During the following days the dose was adjusted to target an INR between 2 and 3. There was a good correlation (r = 0.83, p<0.001) between the INR performed on the morning of day 4 and the daily maintenance dose determined later by successive approximations. This allowed us to write a decisional algorithm to predict the effective maintenance dose of fluindione from the INR performed on day 4. The usefulness and the safety of this approach was tested in a second prospective study on 46 patients receiving fluindione according to the same initial scheme. The predicted dose was compared to the effective dose soon after having reached the equilibrium, then 30 and 90 days after. To within 5 mg (one quarter of a tablet), the predicted dose was the effective dose in 98%, 86% and 81% of the patients at the 3 times respectively. The mean time needed to reach the therapeutic equilibrium was reduced from 13 days in the first study to 6 days in the second study. No hemorrhagic complication occurred. Thus the strategy formerly developed to predict the daily maintenance dose of warfarin from the prothrombin time ratio or the thrombotest performed 3 days after starting the treatment may also be applied to fluindione and the INR measurement.

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