text:
# Citation

Nasiri K, Wrbas KT (2019) Comparing the Effect of Reciproc, ProTaper Next and R-Endo in the Removal of Gutta-percha/Sealer and GuttaFlow during Retreatment. Int J Oral Dent Health 5:087. doi.org/10.23937/2469-5734/1510087

# Comparing the Effect of Reciproc, ProTaper Next and R-Endo in the Removal of Gutta-percha/Sealer and GuttaFlow during Retreatment

##### Kaveh Nasiri1* and Karl-Thomas Wrbas2

1DDS, MSc, Department of Endodontics, Center for Operative Dentistry and Periodontology, University of Dental Medicine and Oral Health, Danube Private University, Krems, Austria

2Professor, Department of Operative Dentistry and Periodontology, Center for Dental Medicine, Oral and Maxillofacial Surgery, Medical Center, University of Freiburg, Freiburg i.Br., Germany; Department of Endodontics, Center for Operative Dentistry and Periodontology, University of Dental Medicine and Oral Health, Danube Private University, Krems, Austria

# Abstract

## Aim

To evaluate the efficacy of three rotary instrumentation systems in removing gutta-percha/sealer and GuttaFlow from root canals and to determine retreatment time.

## Methodology

Sixty palatal roots of extracted first maxillary molars were selected. The samples were prepared with ProTaper Universal and then randomly divided into two groups (n = 30). In groups A and B, the root canals were filled employing lateral compaction of GP/AH Plus and GuttaFlow2, respectively. The samples in each group were randomly divided into three subgroups (n = 10). Groups A1 and B1 were retreated using Reciproc. ProTaper Next was used in groups A2 and B2, whereas groups A3 and B3 were retreated with R-Endo system. Retreatment time was recorded. The roots were split longitudinally and examined under a stereomicroscope and then photographed. The remaining filling material was calculated using Image J software. A two-way analysis of variance (ANOVA) was conducted to examine the effect of three systems in the removal of filling material. Moreover, a Tukey HSD test was used to perform multiple comparisons (α = 0.05).

## Results

Removal of GuttaFlow from the canals was easier and faster than that of GP/AH Plus (p < 0.05). Generally, the results revealed that compared to other systems, R-Endo in group A left less filling material inside the canals (p < 0.05). It also required less time to reach working length than the other systems (p < 0.05). One PTN instrument and two Reciproc instruments were fractured during the retreatment procedures.

## Conclusions

Based on the findings of this study, none of the systems could completely remove the root filling material from the root canals. However, R-Endo was found to be the most effective instrument in the removal of GP/AH Plus.

# Keywords

GuttaFlow, ProTaper Next, Reciproc, R-Endo

# Abbreviations

PTN: ProTaper Next; Rec: Reciproc; PTU: ProTaper Universal; GP: Gutta-percha

# Introduction

The main goal of non-surgical root canal retreatment is the retention of teeth, in order to restore periapical tissue's health and improve patient's quality of life and chewing ability. In this regard, contemporary endodontic techniques in non-surgical root canal retreatment are shown to have satisfactory outcome [1]. The prerequisite for non-surgical root canal retreatment is adequate removal of filling material from root canals in order to enhance cleaning, shaping and filling of the root canals [2]. In a systematic review by Torabinejad, et al. [3] it was reported that orthograde retreatment has a higher success rate (83.0%) than endodontic surgery (71.8%) at 4 to 6 years.

Gutta-percha is the most universally used filling material for the obturation of root canals. It should be removed when secondary therapy is indicated [4]. So far, a number of techniques such as hand instrument, rotary Ni-Ti systems, ultrasonic and laser with or without the use of solvents have been proposed for the removal of root filling material during retreatment procedures [2,5,6]. Previous studies have reported that the removal of filling material was not complete in any of the root canals [2,4]. The apical third is the most probable area to be cleaned and disinfected in the course of successful retreatment as that is the third, where microorganisms generally persist [2,4]. It is worth mentioning that the combined use of different techniques has shown to be more effective than only using one technique for the removal of filling material [4].

Different Ni-Ti systems have been suggested for removing filling material from root canals [7-9]. Retreatment files are specifically designed for the use in retreatment procedures such as R-Endo system. R-Endo system consists of four rotary files and one hand file (Re 25/0.12, R1 25/0.08, R2 25/0.06, R3 25/0.04 and Rm 25/0.04). The cross-section of R-Endo instruments has three equally spaced cutting edges with neither radial lands nor an active tip [7]. Furthermore, Reciproc and ProTaper Next systems were used for the initial root canal therapy, however they can also be used in retreatment procedures [8,9]. Reciproc system has three different sizes: R25 25/0.08, R40 40/0.06 and R50 50/0.05. It has an s-shaped cross-sectional design and a non-cutting tip [8]. As for ProTaper Next, it consists of five Ni-Ti rotary instruments: X1 17/0.04, X2 25/0.06, X3 30/0.07, X4 40/0.06 and X5 50/0.06. PTN files produce an asymmetrical rotation and have a unique rectangular cross-sectional design [9].

Based on literature, comparing different root filling materials during retreatment is one of the most highly researched topics and therefore, it is worth investigating [10]. Thus, in line with literature, this study aimed to evaluate the efficacy of Reciproc, ProTaper Next and R-Endo in the removal of gutta-percha/sealer and GuttaFlow from root canals. Another objective of this study was to determine the time for retreatment. The null hypothesis tested, was that there would be no differences between removal of gutta-percha/sealer and GuttaFlow during retreatment procedures.

# Materials and Methods

Sixty extracted first maxillary molars with single palatal roots and fully formed apices were used in this experimental study. Palatal roots were verified with radiography as having single canals of ≤ 30º curvatures in buccopalatal direction. The canal curvatures were determined employing the Schneider method [11]. Their range was between 0º and 30º with a mean of 14.05º ± 8.37º which indicates that the palatal roots had mild (< 10º), moderate (10-25º) or severe (> 25º) degrees of canal curvatures. The classification of canal curvatures in the present study followed that of the study by Alfouzan and Jamleh [12]. Residues of soft and hard tissues were removed mechanically. The selected samples were immersed in Sodium Chloride 0.9% for 48 hours and then rinsed with distilled water. After access cavity preparation, working length was measured using a size 10 C-Pilot® (VDW, Munich, Germany). In fact, the file was placed into the canal until it was visible at the apical foramen. Also, the working length was established 1 mm shorter of this length.

Regarding the instrumentation of root canals, ProTaper Universal system (Dentsply Sirona, Ballaigues, Switzerland) was used according to the manufacturer instruction with a sequence of SX, S1, S2, F1 and F2 (size 25/0.08 taper). After each instrument, root canals were rinsed with two ml of 2.5% NaOCl. The smear layer was removed with four ml of 17% EDTA within one minute, followed by four ml of distilled water. Subsequently, the canals were dried with paper points and randomly divided into two groups of A and B (n = 30).

Next stage was filling the samples. Samples of group A were filled using lateral compaction technique. Gutta-percha master cones ISO 25 were coated with sealer AH Plus (Dentsply DeTrey, Konstanz, Germany) and inserted into the palatal root canals. Also, a finger spreader was inserted for laterally pack and subsequently, accessory cones were inserted into the canals until they were completely filled. Samples of group B were filled with GuttaFlow2 (Coltene/Whaledent, Langenau, Germany). The convenient syringe delivery system, ROEKO GuttaFlow2 was coated with master cones ISO 25 and slowly inserted into the palatal roots. Subsequently, employing a backfill technique, GuttaFlow was used to fill any additional space that may exist in the canals.

Regardless of root length, the root filling material was homogeneously extended to 12 mm from the apex to the coronal third allowing the use of heatened hand plugger. In addition, the volume of filling material was approximately the same for all palatal roots. Furthermore, access cavities were sealed with temporary filling such as Coltosol F (Coltene/Whaledent, Langenau, Germany). Finally, the teeth were radiographed in buccopalatal direction to determine the quality of the filling procedure. The samples were then stored for two months at 37 ºC in 100% humidity to ensure complete setting of the filling material.

The samples in each group were randomly divided into three subgroups (n = 10) and an ANOVA test was performed to assure that there were no significant differences with regard to the degrees of canal curvatures within the six groups (p = 0.361). Afterwards, the palatal roots were dyed and numbered with three different colors of nail polish (A1: Green, A2: Red, A3: Black; B1: Green, B2: Red and B3: Black).

## Removal of filling material

Groups A1 and B1: In these groups, retreatment procedures were carried out using Reciproc (VDW, Munich, Germany) system. According to the manufacturer's instructions, R25 (size 25/0.08) instrument was used in an up and down motion until reaching working length. Final apical enlargement was performed with R40 (size 40/0.06). Groups A2 and B2: In these groups, filling material was removed using ProTaper Next system (Dentsply Sirona, Ballaigues, Switzerland). X3 (size 30/0.07) and X2 (size 25/0.06) files were used in a crown-down technique. X3 was used for the removal of filling material in the cervical and middle thirds and X2 was used in the apical third. Final apical enlargement was performed with X4 (size 40/0.06).

Groups A3 and B3: In these groups, R1, R2 and R3 files of R-Endo (Micro-Mega, Besancon, France) were sequentially employed. As for the removal of filling material in different areas, R1 files (size 25/0.08) were used in the cervical, R2 (size 25/0.06) and R3 (size 25/0.04) were used in the middle and apical thirds respectively. Final apical enlargement was performed with Revo-S Classic (Micro-Mega, Besancon, France) AS 40/0.06.

A stopwatch was used to measure the retreatment time for each specimen in the three stages: When the working length was reached, when the filling material was completely removed and when the whole process was complete (total time). Retreatment procedures were carried out with an x-smart plus endo-motor (Dentsply Sirona, Ballaigues, Switzerlnad) in all groups. Speed and torque were set for each instrument according to the manufacturer's instructions. All groups had the same irrigation protocol for retreatment. After each instrument, canals were irrigated with 2 ml of 2.5% NaOCl followed by a final rinse with 4 ml of distilled water. Each instrument was discarded after being used in two root canals. The palatal roots were decoronated with a diamond disc up to 12 mm of the reference surface.

Furthermore, the roots were split longitudinally with a diamond disc and both root halves were photographed under a stereomicroscope with 20 X magnification (Bresser, Rhede, Germany). The images were then imported in Image J software (National Institutes of Health (NIH), Bethesda, MD, USA). The root canals were divided into three parts of four mm and the residual filling material in the canal was demarcated. The regions and residual filling material were calculated in mm2. Afterwards, the percentages of residual filling material in the coronal, middle and apical thirds were measured using the following equation: $Fillingmateial\left(%\right)=\frac{areaofresidualfillingmaterial}{areaofcanalwall}×100$

Figure 1 shows an example of the evaluation of residual material via Image J.

Figure 1: Remaining filling material evaluation with Image J software in the canal in the coronal, middle and apical thirds. a) Before analysis; b) After analysis with Image J software. View Figure 1

## Statistical analysis

Statistical analysis was performed with SAS software program (SAS institute Inc., Cary, NC, USA). A two-way analysis of variance (ANOVA) was conducted to analyze the residual filling material among the regions (coronal, middle and apical), systems (Rec, PTN and R-Endo) and between the groups (A and B). Moreover, a Tukey HSD test was applied for pair-wise comparisons (95% confidence intervals). Finally, the retreatment time was analyzed using the above mentioned tests.

# Results

Remnants of filling material were observed in all hemisection samples (Table 1).

Table 1: Shows the mean and standard deviation of each group for remnants of gutta-percha/sealer and GuttaFlow across all systems and regions, as well as the total results. View Table 1

Table 2: Provides mean and standard deviation for the retreatment time (T1, T2 and T3) across all systems and groups. View Table 2

Regarding the coronal third region, the results in group A revealed that R-Endo system left the least residuals of filling material, while PTN system left the highest and this result was statistically significant (p < 0.05). However, no statistically significant difference was observed among the three systems in group B. As for the middle third, there was no statistically significant difference in the residuals of filling material among the three systems and between the two groups (p > 0.05). The results in the apical third of group A showed that R-Endo system left significantly less remnants of filling material than Reciproc and PTN systems (p < 0.05). However, no statistically significant difference was observed among the three systems in group B (p > 0.05). In total, according to the results, the type of system in group A had a significant main effect on the amount of residuals of root filling material. R-Endo system left the least residuals while Reciproc and PTN systems showed significantly higher residuals of filling material (p < 0.05). The specimens in group B, on the other hand, demonstrated no statistically significant difference among the three systems (p > 0.05). Furthermore, GuttaFlow was removed significantly easier than gutta-percha/sealer from the root canals.

Results of the retreatment times were observed in table 2. The results for the first retreatment time in group A revealed that compared to Reciproc and PTN systems, R-Endo system was significantly faster with regard to working length (p < 0.05). In group B, however, Reciproc system required less time than the other two systems (p > 0.05). As for T2 in group A, Reciproc system was found to be significantly slower than PTN and R-Endo systems with regard to the complete removal of filling material (p < 0.05). The mean of the two groups confirmed this result. Regarding T2 in group B, the results showed that the complete removal of the filling material took approximately the same amount of time in all three systems and therefore, no significant difference was found (p > 0.05). The results for T3 in group A indicated that PTN and R-Endo systems were significantly faster than Reciproc (p < 0.05). In group B, however, no significant difference was observed regarding the total time among the three systems. In sum, it can be reported that GuttaFlow was removed significantly faster than gutta-percha/sealer from the root canals.

# Fractured Instruments

Two Reciproc (R 25) instruments with canal curvatures of 29º, 26º and one PTN (X4) instrument with 30º were fractured during retreatment procedures. The broken instruments were successfully removed and the time needed for their removal was not recorded.

# Discussion

The most important stage in the orthograde secondary root canal therapy is the removal of filling material, including an effective debridement and use of irrigation solution on microorganisms that trigger post treatment diseases [13]. The present study examined the effect of Reciproc, ProTaper Next and R-Endo systems in the removal of filling material. In addition, this study aimed to measure and record the retreatment time. In this study, the samples were prepared with ProTaper Universal. PTU is a well-known system for preparation which is made of conventional Ni-Ti alloy and is defined as an active cutting with a convex triangular cross-section for F2 [14]. One of the distinguishing features of the present study is the use of two obturation techniques.

In this study, three different Ni-Ti systems were used for retreatment procedures. Reciproc movement reduces the stress on the instrument allowing the use of counter clockwise and clockwise movements. Reciproc and PTN are produced with M-Wire alloy. M-Wire has higher resistance to cyclic fatigue and therefore, has better flexibility than traditional nickel-titanium [9,15]. However, in the present study three Ni-Ti instruments were fractured. Those were tooth number 6 and 10 in Reciproc system and number 46 in PTN system with canal curvatures of 29º, 26º and 30º respectively. This may be due to the fact that the instruments were used twice or the fact that the three teeth had severe canal curvatures. This result was suggested by previous studies [2,12].

As concluded in previous studies, when the enlargement in retreatment procedures is greater than the initial preparation, the amount of residual filling material in the canal decreases [16,17]. A study conducted by Mohammadzadeh Akhlaghi, et al. [18] showed that preparation with larger size/taper instruments is more effective for cleaning and disinfecting the apical third. Therefore, in the present study, the cross sectional diameters of the final instruments were chosen with larger size. The final preparation was performed with files size 40 to refine the root canal preparation, especially in the apical third. The taper of file size 40 was increased from D0 (diameter) to D1 by 0.06 mm in width and length. The findings of the current study revealed that the ideal file size after retreatment is ISO 40/0.06 taper in straight, mild and moderate canal curvatures.

Retreatment time was recorded in three categories of T1 (to reach WL), T2 (complete removal of filling material) and T3 (total time) as done by Iriboz and Sazak Ovecoglu [10]. Based on the results of this study, all types of rotary Ni-Ti systems in group B required less time in order to remove GuttaFlow compared to the time needed for the removal of the gutta-percha/sealer in group A. This result is consistent with that of Khedmat, et al. study [19].

So far, various methodologies have been used in order to determine residuals of filling material such as rendering transparency [7], x-ray imaging [9], micro-CT [17], cone beam CT [19] and splitting roots longitudinally [20]. Vertical splitting is a well-established and an adequate method, which was employed in this study [21,22]. In this study, the specimens were split vertically and images of the halves were obtained using a stereomicroscope and then evaluated with Image J software. Image J software is a well-known program for analysis of scientific images [23].

According to the data of the results in the present study, GuttaFlow was removed significantly easier from the root canals in group B in comparison to the removal of gutta-percha/sealer in group A. Thus, the null hypothesis tested was rejected. This finding is in line with that of the study conducted by Khedmat, et al. [19]. Furthermore, in group A, more residuals of root filling were observed in the coronal third than in the middle third. As Capar, et al. [16] reported this result might be rooted in the fact that Gates Gliden drills were not used in the coronal third.

Generally, it can be reported that R-Endo system removed gutta-percha and sealer significantly better than other systems which is consistent with the result of Mollo, et al. study [2]. This finding can be attributed to the use of R-Endo retreatment system followed by Revo-S as final preparation. Moreover, the findings of this study showed that none of the Ni-Ti rotary systems completely removed all root filling material from the root canals, which is in agreement with previous studies [13,24].

# Conclusions

Based on the findings of the present investigation, it can be concluded that R-Endo and Revo-S system in group A, were found to be effective in the removal of GP/AH Plus from the root canals. Moreover, R-Endo reached working length faster than Reciproc and PTN systems in group A. Finally, GuttaFlow was removed significantly easier than GP/AH Plus from the root canals.

# Citation

Nasiri K, Wrbas KT (2019) Comparing the Effect of Reciproc, ProTaper Next and R-Endo in the Removal of Gutta-percha/Sealer and GuttaFlow during Retreatment. Int J Oral Dent Health 5:087. doi.org/10.23937/2469-5734/1510087


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# Separation of Variables when one variable depends on another.

Say I have the following PDE ignoring boundary data for the moment $$\frac{\partial^2u(x,y)}{\partial x\partial y}=-u(x,y)\tag1$$ which is similar to the question asked here. Say $u$ is sufficiently smooth and the derivatives could be interchanged.

This equation can be easily solved assuming a separable solution, i.e. $u(x,y)=X(x)Y(y)$. However, what if it is known that $y$ is a function of $x$, $y=y(x)$? Is the equation still separable? Meaning is $u(x,y(x))=X(x)Y(y(x))$ a solution? Could the derivatives still be interchanged?

I have tried various "test functions" that solve the PDE or similar PDEs but have not come to a definitive conclusion. I figured that interchanging the order of the derivatives would lead to different results. For example, integrating out $y$ first would introduce terms with $x$ for the second integration, while integrating along $x$ first would avoid those terms.

Moreover, since $y$ is a function of $x$, heuristically the PDE should be reducible to an ODE. I have attempted this through chain rule. $$\frac{\partial^2u}{\partial x\partial y} =\frac{\partial}{\partial x}\left(\frac{\partial u}{\partial x}\frac{\partial x}{\partial y}\right) = \frac{\partial}{\partial x}\left(\frac{\partial u}{\partial x}\frac{1}{y'}\right) = \frac{\partial^2u}{\partial x^2}\frac{1}{y'}-\frac{y''}{(y')^2}\frac{\partial u}{\partial x}\tag2$$ This would make a second order ODE for $u$. However, when I test this hypothesis nothing seems to be in agreement. For example, let's try $u=x(1-y^2)$ with $y=x^2$ to solve the simpler PDE $$\frac{\partial^2u(x,y)}{\partial x\partial y}=-2y\tag3$$ This $u$ certainly solves $(3)$. Yet when applying the chain rule from $(2)$, it leads to nonsensical results.

This was kind of all over the place. I hope I made my questions clear.

$\boldsymbol{1.}$ Does separation of variables still apply when one variable is dependent on the other?

$\boldsymbol{2.}$ Is smoothness moot in the case that one variable is dependent on the other?

$\boldsymbol{3.}$ What is wrong with my chain rule?

I feel like I am misunderstanding something very fundamental here.

format: plain


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# OHMBetter ISS

##### New member
Hello, when I try to load some SpaceX scenarios I got this ISS error. Is it something to do with your addon?

Here's the log:
============================ ERROR: =========================== Mesh file name not provided [MeshManager::LoadMesh | .\Mesh.cpp | 1237] =============================================================== D3D9: ERROR: D3D9Client::clbkStoreMeshPersistent() hMesh is NULL 000000.000: --------------------------------------------------------------- 000000.000: >>> WARNING: Obsolete API function used: VESSEL::SetBankMomentScale 000000.000: At least one active module is accessing an obsolete interface function. 000000.000: Addons which rely on obsolete functions may not be compatible with 000000.000: future versions of Orbiter. 000000.000: --------------------------------------------------------------- 000000.000: Module SouyzTMA.dll .......... [Build 100902, API 100830] 000000.000: Module Progress_M1.dll ....... [Build 100902, API 100830] 000000.000: Finished initialising status 000000.000: Finished initialising camera 000000.000: Finished setting up render state 000000.000: D3D9: [Scene Initialized] 000000.000: Finished initialising panels ============================ ERROR: =========================== Mesh not found: .\Meshes.msh [LoadMesh | .\Mesh.cpp | 1269] ===============================================================

#### gattispilot

Can u post the scenario?

#### Max-Q

##### 99 40
Hello, when I try to load some SpaceX scenarios I got this ISS error. Is it something to do with your addon?
Doesn’t look like an issue with the ISS. I would suspect either progress or Soyuz… you might try removing them from the scenario and see if it works then.

#### barrygolden

##### Active member
I did load the updated ISS and the astronaut looks super. I think you should have different ones in different positions maybe one who you could fly around but the VC is super and how you move in it. Super job. Not much luck with the EVA stuff though

#### gattispilot

I emailed you. I can help with EVA

#### gattispilot

Here is the EVA module. Attach to the EVA attachment. Here 2 crew are added. You can have 4 max. CREW1 "name of eva" EVA type. This was for the shuttle so we have 2 styles. Non SAFER and SAFER. Default guys are non SAFER. EVA1 is solid red band, EVA2 White bands. EVA3 red stripes, and EVA 4 blue bands. To grap the attachments needs an ID of "HD"
 EVAMODULE:EVAMODULE HATCH 0 0.0000 ft_pad_att_pos 0.0000 0.0000 0.0000 ft_pad_att_dir 0.0000 1.0000 0.0000 ft_pad_att_rot 0.0000 0.0000 -1.0000 ft_pad_att1_pos 0.0000 0.0000 0.0000 ft_pad_att1_dir 0.0000 1.0000 0.0000 ft_pad_att1_rot 0.0000 0.0000 -1.0000 ft_pad_att2_pos 0.0000 0.0000 0.0000 ft_pad_att2_dir 0.0000 1.0000 0.0000 ft_pad_att2_rot 0.0000 0.0000 -1.0000 ft_pad_att3_pos 0.0000 0.0000 0.0000 ft_pad_att3_dir 0.0000 1.0000 0.0000 ft_pad_att3_rot 0.0000 0.0000 -1.0000 STATUS Orbiting Earth RPOS 2830766.201 -6002451.449 1145591.492 RVEL -6833.9462 -2825.5866 2121.6481 AROT -53.098 62.659 -66.476 VROT 0.0654 -0.0000 -0.0000 ATTACHED 0:5,ISS AFCMODE 7 NAVFREQ 0 0 XPDR 0 CREW1 George_D._Nelson SHUTTLEEVA1SAFER CREW2 James_D.A._Van_Hoften SHUTTLEEVA2 END
Focus on EVA or EVA MODULE and CTRL plus Space opens the windows
Important: EVA guy window must be closed prior to entering the vessel or a CTD may occur.

#### Attachments

• EVAMODULE.zip
6.3 MB · Views: 4

#### Max-Q

##### 99 40
v2.4 is released!
Now you can fly through the VC using the S/W keys.

#### barrygolden

##### Active member
I did load the V2.4 and all I can say is WOW !!!!. That new VC and being able to fly through it is as good of addon as I've seen, up there with AMSO and Shuttle Fleet to name a few. I would pay to see someone doing Skylab like that. Awesome work fellows.

#### Max-Q

##### 99 40
I would pay to see someone doing Skylab like that.
Give me a good 3D model and I can do skylab. Personally I would love a nice skylab add on myself… just don’t have the skills to model it. If someone good at modeling wants to help, reach out to me here or by PM.

#### barrygolden

##### Active member
There are some good Skylab's out there but not a real good VC. 4th rock with his Skylab B and others have done Skylab and Skylab 1980 are very fun to use and add some extra stuff and new missions to Fly. I'm looking forward to the MS Saturn's flying soon to use with that.

I can't say enough about ISS A to Z with it's detail and updates that keep it flying so wanted to give a shout out to dommy and all those who worked on that it is super.

Every time I look at this addon I am amazed for it's detail and how user friendly this is. You guys have done a stellar job and the fly around VC , well I don't have the words to describe that. It puts you there inside as one would see if you were there. gattis helped me to add the EVA guys there as well and just blown away with the work done for that, amazing !!!.
Just some thoughts you might need to add the gap spanner from Quest to the truss , some lights and or cameras to cover the station and maybe have the MBS move with the EVA guys on board.

Thanks to all of you that has kept orbiter flying and sharing this with all of us .
Barry

#### Max-Q

##### 99 40
There are some good Skylab's out there but not a real good VC. 4th rock with his Skylab B and others have done Skylab and Skylab 1980 are very fun to use and add some extra stuff and new missions to Fly. I'm looking forward to the MS Saturn's flying soon to use with that.
I could throw a dll at this... no VC, but better than nothing.
Doesn't MS2015 Saturns already work in 2016? Or am I thinking of another addon?

gap spanner from Quest to the truss
What is that?

some lights and or cameras to cover the station
Easy to do if someone has the data on where they go. I really don't like to guess about this kind of thing, personally I think it is better to have a missing feature than an inaccurate feature.

maybe have the MBS move with the EVA guys on board.
The MBS as currently implemented has 4 attachment points. I don't know if gattispilot's EVA astronauts can grab an attachment point, that would be a question for him. I can add more attachments as needed.
You can move the canadarm attached to the MBS.

#### DaveS

##### Space Shuttle Ultra Project co-developer
Donator
Beta Tester
The MBS as currently implemented has 4 attachment points. I don't know if gattispilot's EVA astronauts can grab an attachment point, that would be a question for him. I can add more attachments as needed.
You can move the canadarm attached to the MBS.
The MBS is only for moving the SSRMS, not the astronauts. There's two separate carts for that purpose called the Crew Equipment Translation Aid (CETA) carts. These carts can be attached as train carts to the MT and detached and repositioned as required from the actual ISS truss structure.

#### Max-Q

##### 99 40
There's two separate carts for that purpose called the Crew Equipment Translation Aid (CETA) carts. These carts can be attached as train carts to the MT and detached and repositioned as required from the actual ISS truss structure.
That sounds a bit outside the scope of this addon... Probably just gonna stick to the MBS with canadarm.

#### barrygolden

##### Active member
The gap spanner is a gold hand ladder that the EVA guys use to move from the Quest airlock to the truss. Your right about the MBS and CETA carts so no need to add them or change the MBS function. I found 4 TV/spotlights around the ISS and 1 set of spotlights near the Quest airlock. Thanks from ISS A to Z

#### Attachments

• gap spanner.png
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• g spotlights.png
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• g tv stantion.png
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#### gattispilot

On the CETA I have seen them for the shuttle. Haven't made them yet. The EVA are grap things. The Attachment id needs to be "HD".

#### barrygolden

##### Active member
gattis I think your talking about the PFR's the 2 CETA carts are on the truss of the ISS. They were planned to have the EVA guys ride them to the end of the truss but they found using the hand holds and tether swaps worked fine. they have placed large payloads on them and pulled that out to the work site or ELC's

#### Attachments

• g ceta cart.png
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#### Nikogori

##### Donator
Donator
I like the astronaut in the VC mode! She helps me to understand how large it is inside the space station.
The way she pops out from nowhere reminds me of some horror games, though...

By the way, is it possible to add semi-transparent effect to solar panels?
Default ISS in Orbiter2016 has something like this:

I'm not sure if this is realistic, but this looks nice and shiny.


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# On the moment of inertia of a system of biparticles

1. Nov 6, 2011

### motion_ar

The moment of inertia of a system of particles, is given by:

$$I_i^{\vphantom{^{\:2}}} = \sum_i \; m_i^{\vphantom{^{\:2}}} \, \vec{r}_i^{\:2}$$
The moment of inertia of a system of biparticles, is given by:

$$I_{ij}^{\vphantom{^{\:2}}} = \sum_i \; \sum_{j>i} \; \, m_i^{\vphantom{^{\:2}}} m_j^{\vphantom{^{\:2}}} \; \left( \vec{r}_i - \vec{r}_j \right)^2$$
A system of particles forms a system of biparticles, and from the above equations the following relation can be obtained:

$$I_{ij}^{\vphantom{^{\:cm}}} = M_i^{\vphantom{^{\:cm}}} \: I_i^{\:cm}$$
where $I_{ij}^{\vphantom{^{\:cm}}}$ is the moment of inertia of the system of biparticles, $M_i^{\vphantom{^{\:cm}}}$ is the mass of the system of particles, and $I_i^{\:cm}$ is the moment of inertia of the system of particles relative to the center of mass.

For example, the system of particles A, B, C and D forms the system of biparticles AB, AC, AD, BC, BD and CD.

${\vphantom{aat}}$


text:
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# _______ stock is a class of stock in which the investor has voting rights. A class of

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STAT 2004 WEEK 13  Central limit theorem- No matter the observation distribution, for a large n, x bar ~ N (mu, standard error.) (x bar follows a normal distribution) o This math won’t be tested, but the concept is important.  T-distribution- Has more outliers. Handle problems the same way you would handle a normal distribution, but use the t-table chart. o Degrees of freedom- How many pieces of info It is equal to n-1, and follows the t when written in distribution. For example, if it had 7 degrees of freedom the distribution would be written as t17(mu, S.E.).  The rest of the lecture was essentially going over the hypotheses again. If you are still having trouble with these, remember that finding the p-value is a much easier way to solve the problem. If the p-value is less than alpha, reject the null hypothesis.

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Homework Help: Isobaric compression from isotherm to adiabat

1. Sep 1, 2012

nlingraham

1. The problem statement, all variables and given/known data

The figure(Figure 1) shows a thermodynamic process followed by 150 mg of helium. Determine the pressure (in atm) at points 1, 2, and 3. Determine the temperature (in °C) at points 1, 2, and 3.

http://imgur.com/B7lwQ

n=.0375 mol
P1=3 atm
P2=1 atm
T1=971.85 k
T2=971.85 k
V1=1000 cm^3
V2=V3=3000 cm^3

2. Relevant equations

PV=nRT

3. The attempt at a solution

I'm only on the pressure part right now. From the given chart P1=3 atm. I used PV=nRT, and got that T1 and T2 are 971.85 K. With that, I used ideal gas law again to get that P2=1 atm. However, I don't know how to get the pressure at point 3 since I don't know the temperature at that point. It looks like it goes through an isobaric compression from the isotherm to the adiabat to me. Any help is appreciated.

(303000)(.001)=(.0375)(8.314)T, T1=T2=971.85 K

P(.003)=(.0375)(8.314)(971.85), P2=1 atm

Last edited: Sep 1, 2012
2. Sep 1, 2012

rock.freak667

From 1 to 3, the He goes through an adiabatic process such that

PVγ= constant

So you will have to use this to get P3

3. Sep 1, 2012

nlingraham

Ok, I get the PVγ, where γ=5/3 since its a monatomic gas, but what exactly is the constant? Is that supposed to be nR?

4. Sep 1, 2012

nlingraham

Ok, I think I got it. So it would be P2V2γ=P1V1γ and then just solve for P2

5. Sep 1, 2012


text:
# If p is prime, prove the group (Zp*,x) has exactly one element of order 2.

1. Nov 26, 2011

### ae1709

Hi. I need to: prove the group (Zp*,x) has exactly one element of order 2. Here, p is prime and (Zp*,x) is the set {1, 2,....., p-1} under multiplication modulo p. Any help would be much appreciated!

2. Nov 26, 2011

### Office_Shredder

Staff Emeritus
I think the easier half is: which element has order two?

It might help if you write down the condition of what it means to have order 2

3. Nov 26, 2011

### micromass

Something that might help you is knowing that $\mathbb{Z}_p^*$ is cyclic. Do you know this already??

4. Nov 26, 2011

### micromass

If you do not know the previous. Then you might want to think about the polynomial $X^2-1$ in $\mathbb{Z}_p[X]$. What do you know about its roots??


text:
Math Help - De moivres theorem

1. De moivres theorem

Simplify the following

A) (cosx - isinx)^5
B) (sinx - icosx)^4

for A i get

cos5x - isin5x
I think this is right...?

not sure if B is done the same or not. any help?

2. Hello,
Originally Posted by djmccabie
Simplify the following

A) (cosx - isinx)^5
B) (sinx - icosx)^4

for A i get

cos5x - isin5x
I think this is right...?

not sure if B is done the same or not. any help?
Here is what you can do

De Moivre's formula says : $(\cos(x)+i\sin(x))^n=\cos(nx)+i \sin(nx)$

Remember that the sine function is odd and the cosine function is even.
So $(\cos(x)-i\sin(x))^n=(\cos(-x)+i \sin(-x))^n=$ $\cos(-nx)+i \sin(-nx)=\cos(nx)-i \sin(nx)$

3. so did i do it right :S

is it different when cosine and sine are switched round?

thanks

4. Originally Posted by djmccabie
so did i do it right :S

is it different when cosine and sine are switched round?

thanks
Yes, it's the correct result.

If they're switched... do you mean $(-\cos(x)+i \sin(x))^n$ ?
Then it's just $(-1)^n (\cos(x)-i\sin(x))^n=(-1)^n(\cos(nx)-i\sin(nx))$

5. hi thanks for helping me. its actualyy (sinx - icosx) does this change things??

6. Originally Posted by djmccabie
hi thanks for helping me. its actualyy (sinx - icosx) does this change things??
Yes :

$\sin(x)-i \cos(x)$
Multiply and divide by i :

$\frac 1i \left(i [\sin(x)-i\cos(x)]\right)=\frac 1i (\cos(x)+i \sin(x))$

So $(\sin(x)-i \cos(x))^n=\frac{1}{i^n} (\cos(nx)+i \sin(nx))$


text:
# Placing text inside graphs using pgfplot

My node markers disappear using this code. Is there a better way to do this?

\documentclass{article}
\usepackage{amsmath}
\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}[domain=0:3]
\begin{axis}[xlabel=Frequency(GHz), ylabel=Output Power(dBm)]
table[x=x,y=y] {
x         y
100  12.9
130  7.7
140  8
144  5
150  6.3
150  12.2
213  -3.2

};
\node[red,above] at (axis cs:102,12.9){\small{'12 MTT}};
\node[red,below] at (axis cs:104,12.9){\small{65nm CMOS}};

\node[red,left] at (axis cs:130,7.7){\small{'12 MWCL}};
\node[red,below left] at (axis cs:130,7.7){\small{0.13$\mu$m CMOS}};

\end{axis}
\end{tikzpicture}
\end{document}

• add clip=false in the {axis} options – vrleboss Jun 18 '13 at 19:07
• instead of putting two nodes for your two line of text, you could write: \node[red,above,text width = 3cm] at (axis cs:102,12.9){\small{'12 MTT\\65nm CMOS}}; See: tex.stackexchange.com/questions/119366/… – vrleboss Jun 18 '13 at 20:08

The quick fix would be to set either clip=false or clip mode=individual in the axis options. However, this can have undesired effects if your plot data exceeds the axis limits or if you have several plots with lines and markers.

The "proper" way would be to wrap the \node commands in \pgfplotsset{after end axis/.append code={ ... } }. That way, the commands will be executed after the clip path has been deactivated.

\documentclass{article}
\usepackage{amsmath}
\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{axis}[xlabel=Frequency(GHz), ylabel=Output Power(dBm)]
table[x=x,y=y] {
x         y
100  12.9
130  7.7
140  8
144  5
150  6.3
150  12.2
213  -3.2

};

\pgfplotsset{
after end axis/.code={
\node[red,above] at (axis cs:102,12.9){\small{'12 MTT}};
\node[red,below] at (axis cs:104,12.9){\small{65nm CMOS}};

\node[red,left] at (axis cs:130,7.7){\small{'12 MWCL}};
\node[red,below left] at (axis cs:130,7.7){\small{0.13$\mu$m CMOS}};
}
}

\end{axis}

\end{tikzpicture}
\end{document}

• @vrleboss: Because the plots will still be clipped. Try setting xmax=180 in both solutions. – Jake Jun 18 '13 at 19:54

It seems that you are splitting your nodes in two to have the text on two lines.

To do so you could use the method described here: tikz alignment for multi-line text within font commands to get your node text on multiple lines.

Also you could use the pin option of the nodes: (you can find nice examples here: pgf(plots) node shadow/opaque pin)

\documentclass{article}
\usepackage{amsmath}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}[domain=0:3]
\begin{axis}[xlabel=Frequency(GHz), ylabel=Output Power(dBm)]
table[x=x,y=y] {
x         y
100  12.9
130  7.7
140  8
144  5
150  6.3
150  12.2
213  -3.2

};

\pgfplotsset{
after end axis/.code={
\node[style={fill=blue,circle,inner sep=0pt,minimum size=4pt},pin={[text=red,text width=3cm,pin edge={black,thick}]180-45:{\small{'12 MTT\\65nm CMOS}}}] at (axis cs:102,12.9) { };
\node[style={fill=blue,circle,inner sep=0pt,minimum size=4pt},pin={[text=red,text width=3cm,pin edge={black,thick}]45:{\small{'12 MWCL\\0.13$\mu$m CMOS}}}] at (axis cs:130,7.7){ };

}
}

\end{axis}
\end{tikzpicture}
\end{document}

• How do you set the pin edge length? – JFernan Dec 5 '16 at 17:31


text:
# [texhax] very long nested expressions in math-mode

Torsten Anders torstenanders at gmx.de
Mon Oct 17 15:20:18 CEST 2005

Dear all,

Firstly, I should mention that I am new to this list. I read the FAQ
and quite some docomentation to find an answer to my problem, without
success unfortunately. Nevertheless, I apologise in case I missed
something obvious.

I want to transform program source examples into mathematical notation
in Latex (tetex, i.e. incl. AMS packages), because that way the
examples become more concise and better to communicate. Because the
source is based on functional and logic programming, the available
algorithm packages are less suited -- the result is too easily misread
as procedural programming. Instead, I would prefer to write plain math
expressions.

In short, my problem is that I need to write rather long expressions
(e.g. highly nested and with long variable names for
comprehensibility). Thus, line breaks are inevitable. Naturally, the
continued expression should be indented to indicate the nested
structure of the expression. That is, I don't what to mechanically
indent by a certain amount (e.g. by \quad), but the indentation should
depend on the indentation depth of the surrounding, e.g., function
call. For instance, a short dummy example may read like this:

xs = find(map([1, 2, 3],
f : f(x) = x^3),
isEven)

The most easy way to do something like this is probably to use
mono-space fonts in some verbatim environment. However, I would prefer
to write my example in Latex's math mode: e.g., I would prefer to use
signs like \vee, \wedge, \bigwedge etc.

To avoid getting lost in my own long Latex examples, I would like to
define some suitable Latex command, e.g., to get the example above I
would like to write something like

$xs = \Apply{find}{\Apply{map}{[1,2,3], \\ f : f(x) = x^3}, \\ isEven}$

So far I did not find a way to define \Apply as above and get a
suitable output. In the following, I present a few of my attempts to
set my examples. However, none of what I came up with so far is really
satisfying. Perhaps anybody here can help me..

Here comes my first naive attempt to define \Apply:

\newcommand{\Apply}[2]{\ensuremath{#1 ( \begin{aligned}[t] #2
\end{aligned} ) }}

which is called

$xs = \Apply{find}{&\Apply{map}{&[1,2,3], \\ &f : f(x) = x^3}, \\ &isEven}$

actual problem is that everything after the aligned environment (i.e.
the comma and the cloing parenthesis) 'go back' on the original line
like

xs = find(map([1, 2, 3],	 ),)
f : f(x) = x^3
isEven

Next try:

\newcommand{\Apply}[3]{\ensuremath{#1 ( \begin{aligned}[t] #2 ) #3
\end{aligned} }}

$xs = \Apply{find}{&\Apply{map}{&[1,2,3], \\ &f : f(x) = x^3}{,} \\ &isEven}{}$

This results in the desired output, but for complex examples with
parenthesis/brackets/curly braces in the third \Apply argument this
becomes very hard to read and the editor (i.e. emacs) can't help
anymore.

To avoid the problem that after a box -- which starts at the current
line but introduces some line breaks -- the current line is _not_
continued I tried to center the whole expression:

\newcommand{\Apply}[2]{\ensuremath{#1 \left( \begin{aligned} #2
\end{aligned} \right) }}

$xs = \Apply{find}{&\Apply{map}{&[1,2,3], \\ &f : f(x) = x^3}, \\ &isEven}$

The structure of the resulting expression is still clearly readable and
the code is also more easy to write. However, this layout can also
the parenthesis look more like a binom (and reducing the gap between
the function name and the parenthesis does not really overcome that).
:-P

Does anybody have a better idea how to set very long nested
expressions? Any help is most appreciated!

Best wishes,
Torsten

--
Torsten Anders
Sonic Arts Research Centre
Queen's University Belfast (UK)
www.torsten-anders.de


text:
It is currently 27 Feb 2020, 12:55

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# For the rectangular solid below, ﬁnd the following. (a) Surf

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For the rectangular solid below, ﬁnd the following. (a) Surf [#permalink]  26 May 2019, 10:28
Expert's post
For the rectangular solid below, ﬁnd the following.

(a) Surface area of the solid

(b) Length of diagonal AB

Attachment:

#GREexcercise For the rectangular solid below, ﬁnd the following.jpg [ 20.01 KiB | Viewed 2730 times ]

[Reveal] Spoiler: OA
(a) 208 (b) $$3 \sqrt{17}$$

Math Review
Question: 14
Page: 262
Difficulty: medium

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Re: For the rectangular solid below, ﬁnd the following. (a) Surf [#permalink]  26 May 2019, 18:37
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Carcass wrote:
For the rectangular solid below, ﬁnd the following.

(a) Surface area of the solid

(b) Length of diagonal AB

Attachment:
#GREexcercise For the rectangular solid below, ﬁnd the following.jpg

[Reveal] Spoiler: OA
(a) 208 (b) $$3 \sqrt{17}$$

Math Review
Question: 14
Page: 262
Difficulty: medium

Here,

Surface area of the solid is = $$2(LH + BH + LB) = 2 (70 + 20 + 14) = 2(104) = 208$$

Length of AB = $$\sqrt{{L^2 + B^2 + H^2}} = \sqrt{{ 49 + 4 + 100}}= \sqrt{153} = 3\sqrt{17}$$
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Re: For the rectangular solid below, ﬁnd the following. (a) Surf [#permalink]  30 Oct 2019, 13:51
any explain how the length of AB is calculated? Looking for an explanation to pranab's solution.

thanks!
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Re: For the rectangular solid below, ﬁnd the following. (a) Surf [#permalink]  30 Oct 2019, 14:40
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Expert's post
bellavarghese wrote:
any explain how the length of AB is calculated? Looking for an explanation to pranab's solution.

thanks!

It's based on a useful formula, which goes something like this:

If you have a box with dimensions A x B x C, and points P and Q are located as shown in the diagram, then the length of PQ $$= \sqrt{A^2 + B^2 + C^2}$$

Cheers,
Brent
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Re: For the rectangular solid below, ﬁnd the following. (a) Surf   [#permalink] 30 Oct 2019, 14:40
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text:
PolynomialInterpolation - Maple Help

Student[NumericalAnalysis]

 PolynomialInterpolation
 perform polynomial interpolation on a set of data

 Calling Sequence PolynomialInterpolation(xy, opts)

Parameters

 xy - list(numeric), list(list(numeric, numeric)), list(list(numeric, numeric, numeric)); the data points to be interpolated opts - equation(s) of the form keyword=value where keyword is one of digits, errorboundvar, extrapolate, function, independentvar, method; the options for interpolating the data xy

Options

 • digits = posint
 A positive integer; the environment variable Digits will be set to this integer during the execution of this procedure. By default, digits = 10.
 • errorboundvar = name
 The name to assign to the variable in the errorbound term.
 • extrapolate = algebraic, list(algebraic)
 The points to be extrapolated. By default no points are extrapolated. To see the extrapolated values after using the PolynomialInterpolation command, use the ExactValue or ApproximateValue command.
 • function = algebraic
 The exact function to use when computing the absolute error. If only the x data is given in xy, the function must be specified by the user, or an exception will be raised. By default, no function is used.
 • independentvar = name
 The name to assign to the independent variable in the interpolant. If independentvar is not specified, the independent variable in function will be used.  If function and independentvar are both unspecified, ind_var will be used as the independent variable in the interpolant.
 • method = hermite, lagrange, neville, newton
 The method to use when performing the polynomial interpolation.
 – hermite : Hermite Interpolation; this method requires xy to be in the form [[${x}_{1}$, ${y}_{1}$, ${p}_{1}$], [${x}_{2}$, ${y}_{2}$, ${p}_{2}$],...].
 – lagrange : Lagrange Form Interpolation
 – neville : Neville's Algorithm
 – newton : Newton Interpolation
 If no method is specified by the user, the Lagrange method will be used.  However, if xy is of the form list(numeric, numeric, numeric) and the user does not specify a method, the Hermite method will be used.

Description

 • The PolynomialInterpolation command interpolates the given data points xy and stores all computed information in a POLYINTERP structure.
 • The POLYINTERP structure is then passed around to different interpolation commands in the Student[NumericalAnalysis] subpackage where information can be extracted from it and, depending on the command, manipulated.

Notes

 • When the Hermite method is used to perform interpolation, xy must be of the form list(list(numeric, numeric, numeric)).
 • This procedure operates numerically; that is, inputs that are not numeric are first evaluated to floating-point numbers before computations proceed.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{NumericalAnalysis}\right]\right):$
 > $\mathrm{xy}≔\left[\left[0,1\right],\left[\frac{1}{2},1\right],\left[1,\frac{11}{10}\right],\left[\frac{3}{2},\frac{3}{4}\right],\left[2,\frac{7}{8}\right],\left[\frac{5}{2},\frac{9}{10}\right],\left[3,\frac{11}{10}\right],\left[\frac{7}{2},1\right]\right]$
 ${\mathrm{xy}}{≔}\left[\left[{0}{,}{1}\right]{,}\left[\frac{{1}}{{2}}{,}{1}\right]{,}\left[{1}{,}\frac{{11}}{{10}}\right]{,}\left[\frac{{3}}{{2}}{,}\frac{{3}}{{4}}\right]{,}\left[{2}{,}\frac{{7}}{{8}}\right]{,}\left[\frac{{5}}{{2}}{,}\frac{{9}}{{10}}\right]{,}\left[{3}{,}\frac{{11}}{{10}}\right]{,}\left[\frac{{7}}{{2}}{,}{1}\right]\right]$ (1)
 > $L≔\mathrm{PolynomialInterpolation}\left(\mathrm{xy},\mathrm{independentvar}=x,\mathrm{method}=\mathrm{lagrange}\right):$
 > $\mathrm{Nev}≔\mathrm{PolynomialInterpolation}\left(\mathrm{xy},\mathrm{independentvar}=x,\mathrm{method}=\mathrm{neville}\right):$
 > $\mathrm{New}≔\mathrm{PolynomialInterpolation}\left(\mathrm{xy},\mathrm{independentvar}=x,\mathrm{method}=\mathrm{newton}\right):$
 > $\mathrm{expand}\left(\mathrm{Interpolant}\left(L\right)\right)$
 ${1}{+}\frac{{2254}}{{75}}{}{{x}}^{{2}}{+}\frac{{733}}{{20}}{}{{x}}^{{4}}{-}\frac{{3296}}{{225}}{}{{x}}^{{5}}{+}\frac{{221}}{{75}}{}{{x}}^{{6}}{-}\frac{{53}}{{225}}{}{{x}}^{{7}}{-}\frac{{172247}}{{3600}}{}{{x}}^{{3}}{-}\frac{{8183}}{{1200}}{}{x}$ (2)
 > $\mathrm{expand}\left(\mathrm{Interpolant}\left(\mathrm{Nev}\right)\right)$
 ${1}{+}\frac{{2254}}{{75}}{}{{x}}^{{2}}{+}\frac{{733}}{{20}}{}{{x}}^{{4}}{-}\frac{{3296}}{{225}}{}{{x}}^{{5}}{+}\frac{{221}}{{75}}{}{{x}}^{{6}}{-}\frac{{53}}{{225}}{}{{x}}^{{7}}{-}\frac{{172247}}{{3600}}{}{{x}}^{{3}}{-}\frac{{8183}}{{1200}}{}{x}$ (3)
 > $\mathrm{expand}\left(\mathrm{Interpolant}\left(\mathrm{New}\right)\right)$
 ${1}{+}\frac{{2254}}{{75}}{}{{x}}^{{2}}{+}\frac{{733}}{{20}}{}{{x}}^{{4}}{-}\frac{{3296}}{{225}}{}{{x}}^{{5}}{+}\frac{{221}}{{75}}{}{{x}}^{{6}}{-}\frac{{53}}{{225}}{}{{x}}^{{7}}{-}\frac{{172247}}{{3600}}{}{{x}}^{{3}}{-}\frac{{8183}}{{1200}}{}{x}$ (4)
 > $\mathrm{xyyp}≔\left[\left[1,1.105170918,0.2210341836\right],\left[1.5,1.252322716,0.3756968148\right],\left[2,1.491824698,0.5967298792\right]\right]$
 ${\mathrm{xyyp}}{≔}\left[\left[{1}{,}{1.105170918}{,}{0.2210341836}\right]{,}\left[{1.5}{,}{1.252322716}{,}{0.3756968148}\right]{,}\left[{2}{,}{1.491824698}{,}{0.5967298792}\right]\right]$ (5)
 > $\mathrm{p2}≔\mathrm{PolynomialInterpolation}\left(\mathrm{xyyp},\mathrm{method}=\mathrm{hermite},\mathrm{function}=\mathrm{exp}\left(0.1{x}^{2}\right),\mathrm{independentvar}=x,\mathrm{errorboundvar}=\mathrm{\xi },\mathrm{digits}=5\right):$
 > $\mathrm{RemainderTerm}\left(\mathrm{p2}\right)$
 $\left(\frac{\left({0.120}{}{{ⅇ}}^{{0.1}{}{{\mathrm{\xi }}}^{{2}}}{+}{0.0720}{}{{\mathrm{\xi }}}^{{2}}{}{{ⅇ}}^{{0.1}{}{{\mathrm{\xi }}}^{{2}}}{+}{0.00480}{}{{\mathrm{\xi }}}^{{4}}{}{{ⅇ}}^{{0.1}{}{{\mathrm{\xi }}}^{{2}}}{+}{0.000064}{}{{\mathrm{\xi }}}^{{6}}{}{{ⅇ}}^{{0.1}{}{{\mathrm{\xi }}}^{{2}}}\right){}{\left({x}{-}{1.}\right)}^{{2}}{}{\left({x}{-}{1.5}\right)}^{{2}}{}{\left({x}{-}{2.}\right)}^{{2}}}{{720}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&where}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left\{{1.}{\le }{\mathrm{\xi }}{\le }{2.}\right\}$ (6)
 > $\mathrm{DividedDifferenceTable}\left(\mathrm{p2}\right)$
 $\left[\begin{array}{cccccc}{1.1052}& {0}& {0}& {0}& {0}& {0}\\ {1.1052}& {0.22103}& {0}& {0}& {0}& {0}\\ {1.2523}& {0.29420}& {0.14634}& {0}& {0}& {0}\\ {1.2523}& {0.37570}& {0.16300}& {0.033320}& {0}& {0}\\ {1.4918}& {0.47900}& {0.20660}& {0.043600}& {0.010280}& {0}\\ {1.4918}& {0.59673}& {0.23546}& {0.057720}& {0.014120}& {0.0038400}\end{array}\right]$ (7)
 > $\mathrm{Draw}\left(\mathrm{p2}\right)$