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Screen shot #12 (Merely a picture to illustrate that our GUI is totally self-explanatory)

Click here to go to our overview of Atmospheric Models.

Click here to go to our discussion of Robust Control Topics.

Click here to see a sampling of topics discussed and our style of doing so within our self-contained TK-MIP.

Click here to go to our relevant Anagrams and Palindromes.

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Dr. Paul J. Cefola, the expert referenced above, has a consultancy in Sudbury, Massachusetts: cefola “at” comcast.net.

 Click here to get the (draft copy) of AIAA Standards for Atmospheric Modeling, as specified by the various U.S.and other International agencies.

With Prompters_On, we are less diplomatic and say what we really think (and can back-up)! Work on Robust Control over a decade and a half by the mid 1990's could merely handle Linear Time Invariant (LTI) systems with no nonlinearities, no time-varying parameters, and no noise disturbances present. The only disturbance Robust Control could handle successfully was a persistent constant bias offset. The real world is nonlinear and, even when locally linearized, it is usually properly modeled as being time-varying in general. One prominent Laboratory for Information and Decision Systems (LIDS) formulation at MIT for Robust Control (Lopez, J. E., Athans, M, “On Synthesizing Robust Decentralized Control,” American Control Conference, 1994-TK7855.M41.E3845 no. 2197 at Barker Library at MIT) requires that the system state dimension, the number of components of the output measurements, and the number of components of the control all be of the same exact dimension in common as well as the system being just LTI. This formulation is not very realistic (as an understatement since most systems will not exhibit these characteristics). Yet TK-MIP still reports here on the best that it has found that: (1) heroically handles one scalar nonlinearity in an otherwise LTI system; (2) heroically handles one scalar time-varying parameter in an otherwise LTI system; and (3) heroically handles one scalar noise component in an otherwise LTI system. None of these Robust Control formulations can yet handle all three of these situations simultaneously. Therefore Robust Control is evidently a much less capable methodology than what can be routinely handled in a straightforward manner within existing standard prior state variable formulations. LTI is needed to apply the Robust Control methodology since the new toy for these analysts, consisting of left and right lambda matrix factorizations, are performed in the frequency domain. By being so very conservative (in a minimax sense) by how Robust Control handles system control aspects by single-mindedly focusing on the worse case system characteristics and then by trying to do the best it can with the worse aspects, the subsequent system response is typically very, very sluggish! Few real applications can tolerate such unpleasantly slow response characteristics except, perhaps, in process control. This limited applicability should be emphasized more in the Robust Control literature as a standard disclaimer to the unwary. To date, this has not happened. TeK Associates is aware that, in 2009, there are about 40 books on how to apply Robust Control to applications. If the only objective is a ticket to a technical conference to present a paper on the subject, then this topic is germane. If the objective is to solve real-world problems in a timely manner with realistic resources (as historically had been the goal), then  perhaps use of Robust Control is not the path to follow. (TeK Associates has even actually overheard [in a public forum prior to the speaker going to participate in a crew event that weekend at “The Head of the Charles Regatta” (at Harvard University but the meeting where this event took place was not at Harvard)] this visiting Robust Control and Intelligent Control researcher’s flim-flam artist-like response to project funders at the end of the rainbow (to allow the researcher to save face): “Oops, the resulting solution is, unfortunately NP-hard, and therefore not tenable. Sorry!”, as he rehearsed and “broadcast as a shout out” for others to use as well in similar situations or circumstances. Talk about “biting the hand that feeds you!” Is this not welfare for Ph.D.’s? In a bygone era, control theorists used their considerable intellect to actually improve the world. Who, with undue or unwarranted influence, lead them so far astray? Fortunately or unfortunately, TeK Associates thinks it knows the answer. What was muttered in antiquity at the walls of Troy, at the sight of the large wooden horse?  

With the apparent current lack of technical integrity and adequate oversight in a closed club, is it any wonder the U.S. is in its current predicament?) [Well that pretty much proves that I have the jaw bone of an ass.... Now all I need to do is to let my hair grow longer and find a Delilah. Finding one shouldn't be too hard since so many of them abound.]

At the 1992 (or was it 1998?) Conference on Decision and Control, a Robust Control Design Challenge was levied, and several investigators rose to the challenge and submitted abstracts promising solutions to be presented at the subsequent year’s Conference on Decision and Control. The authors who planned to participate with their solutions looked like a who’s who in modern control. Despite the simplicity of the low dimensional example comprising the system to be designed for robust control, every anticipated presenter has a void in the proceedings of this subsequent year’s conference where the promised solutions should have appeared. What an embarrassment! This should have been a reality check early on regarding problems with the robust control methodology.

Although the late George Zames is credited in a moving (and extremely informative) tribute by Prof. Sanjoy Mitter on pp. 590-595 in the May 1998 issue of IEEE Trans. on Automatic Control with, essentially, single-handedly bringing mathematical functional analysis to the aid of control and system theory via use of the contraction mapping principle (CMP) in Zames, G., “Feedback and Optimal Sensitivity: model reference transformations, multiplicative semi-norms, and approximate inverses,”  IEEE Trans. on Auto. Contr., Vol. 26, pp. 744-752, Apr. 1981. (see Bensoussan, A., Stochastic Control by Functional Analysis Methods, Vol. II, North-Holland Publishing, NY, 1982 and see Kreyszig, E., Introductory Functional Analysis with Applications, John Wiley & Sons, NY, 1978), please peruse the earlier contribution by Jack M. Holtzman’s (Bell Telephone Lab., Whippany, NJ) Nonlinear System Theory: A Functional Analysis Approach, Prentice-Hall, 1970, which also has the use of CMP as its main theme in such systems. However, Holtzman worked everything out in detail in the above cited book so that his results were on a platter in such a form that they could be easily understood and conveniently applied immediately to practical system design by engineering readers faced with real applications and who may not necessarily be interested in abstract results in a technical paper whose significance is not known until several years later. Charles Desoer’s and M. Vidyasagar’s (U. C., Berkley) textbook came out several years earlier than Zames too and also had a functional analysis bent. A. V. Balakrishnan (UCLA) has also been an avid practitioner of functional analysis in analyzing the behavior of systems and in understanding optimal control (including his contributions to numerical solution algorithms) since the early 1960’s. There is even another precedent for utilizing a contraction mapping to converge to the fixed point solution in: Kerr, T. H., “Real-Time Failure Detection: A Static Nonlinear Optimization Problem that Yields a Two Ellipsoid Overlap Test,” Journal of Optimization Theory and Applications, Vol. 22, No. 4, pp. 509-535, August 1977. Again for MIT, the well-known Not Invented Here (NIH) syndrome seems to be at play  (i.e., only cite work from people affiliated with MIT in some way and ignore the rest even if they had priority in their results). With this, I keep my personal promise to the late Dr. Harold Chestnut, VP at General Electric in Schenectady, NY in the early 1970’s, to be vigilant on these issues (see Chestnut, H., “Bridging the Gap in Control - Status 1965,” IEEE Trans. on Automatic Control, Vol. 10, pp. 125-126, Apr. 1965 [and evidently still a problem today]).

We at TeK Associates are positive about the status of control theory in general and are optimistically enthusiastic about:

Bossert, D. E., Lamont, G. B., Horowitz, I., “Design of Discrete Robust Controllers using Quantitative Feedback Theory and a Pseudo-Continuous-Time Approach,” on pp. 25-31 in Osita D. T. NWOKAH (Ed.), Recent Developments in Quantitative Feedback Theory: Work by Prof. Issac Horowitz (predating research in Robust Control by two decades), presented at the winter annual meeting of the American Society of Mechanical Engineers,  Dallas, TX, 25-30 Nov. 1990;

Barnard, R., “A Quantitative Feedback Theory Based on Time Domain and Fixed Point Notions (as a consequence of contraction mappings encountered),” on 45ff. in Osita D. T. NWOKAH (Ed.), Recent Developments in Quantitative Feedback Theory: Work by Prof. Issac Horowitz, presented at the winter annual meeting of the American Society of Mechanical Engineers,  Dallas, TX, 25-30 Nov. 1990;

Intelligent Control and Adaptive Systems, Ed./Chair Guillermo Rodriguez, Proceedings of SPIE-The International Society for Optical Engineering, Vol. 1196, Bellingham, WA, 7-8 Nov. 1989;

Butkovskiy, A. G., Pustyl'nikov, A. M., Mobile Control of Distributed Parameter Systems, Ellis Horwood Ltd., Chichester, Halstead Press, division of John Wiley, NY, 1997 (especially see Appendix 6 for 23 varieties of Integral Transforms on pp. 249-267; Appendix 7: Sobolev Transform; Appendix 12: On an Approximation Investigation of Mobile Control Problems for Distributed Control);

Becedas, J., Mamani, G., Feliu, V., Siva-Ramirez, H., “Estimation of Mass-Spring-Damper System,” in Advances in Computational Algorithms and Data Analysis, S.-I. Ao, B. Kieger, S.-S. Chen (Eds.), Springer Science & Business Media, 2009;

Schlacher, K., Irschik, H., Kugi, A., “Control of Nonlinear Beam Vibrations by Multiple Piezoelectric Layers,” pp. 355-362 in IUTAM Symposium on Interaction between Dynamics and Control in Advanced Mechanical Systems, D. H. VanCampen (Ed.), Kluwer Academic Publishers, Netherlands, 1997;

Hajek, O., Control Theory in the Plane, 2nd Edition, Lecture Notes in Control and Information Sciences, Springer-Verlag, NY, 2009;

Ching, S.-N., Eun, Y., Gokcek, C., Kabamba, P. T., Meerkov, S. M., Quasilinear Control: Performance analysis and design of feedback systems with nonlinear sensors and actuators, Cambridge University Press, Cambridge, UK, 2011.

To complete the expose started above, recall the creatively designed endeavor below which featured a multiple model bank of N Kalman filters in parallel with an LQ feedback regulator control law for each Kalman filter equipped feedback branch after which the aggregated net result of the particular scalar weightings consisting of the individual probabilities, as calculated on-line in real-time, and corresponding to any particular branch of the LQG being correctly associated with the present mode (of only N different possible modes being modeled) for the actual multi-mode system under consideration:

Athans, M., Castanon, D., Dunn, K.-P., Lee, W. H., Sandell, N. R., Willsky, A. S., “The Stochastic Control of the F-8C Aircraft using a Multiple Model Adaptive Control (MMAC) method - I: Equilibrium Flight,” IEEE Trans. on Automatic Control, Vol. 22, No. 5, pp. 768-780, Oct. 1977. Was non-equilibrum flight ever considered or handled (where non-equilibrium flight is take-offs and landings and dog fight maneuvers or even maneuvers as benign as just coordinated turns)? Did this approach actually work? Was there ever a Phase II follow-on thus indicating success of the particular approach? The answer appears to be “no” on all three counts. This constitutes a high profile publicity stunt or charade without any useful payoff to the NASA customer. This was business as usual in some circles! I definitely would like to chase the money changers from the temple (of learning and useful knowledge). If they had not been pretending so hard that LQG theory was not fatally flawed, they could have equipped each LQG leg with a stable replacement LQG/Loop Transfer Recovery, as its correction. The resulting redesign may now actually work as they had hoped the initial version would.

Perhaps the funniest situation was when several people complained that the IEEE TAC paper review system was, perhaps, apparently being abused by reviewers or assistant editors being the first to see and then recognize a significant new result and then dispatch a graduate student (among an ample pool of available talent) to either use the topic of the paper under review as their thesis or write a paper on the topic themselves and then submit it for publication even before the original paper had appeared for the first time in print (a process that took about two years in those days). Afterwards, people at a particular institution would just reference the work of the authors affiliated with the same institution and ignore the true originator (who should have been acknowledged as having had the precedent) as yet another example of the NIH syndrome. What was funny was who was on the two man committee to look into the possible problem and who reported his conclusions that everything regarding the current IEEE TAC review process was just fine! Isn't that particular situation like “having the fox guard the chicken coop?”

Another variation of sorts of the dreaded NIH syndrome, discussed above, occurs in the following:

Smith, S. T., “Statistical Resolution Limits and the Complexified Cramer-Rao Bound,” IEEE Trans. on Signal Processing, Vol. 53, No. 5, pp. 1597-1609, May 2005.

Smith, S. T., “Covariance, Subspace, and Intrinsic Cramer-Rao Bounds,” IEEE Trans. on Signal Processing, Vol. 53, No. 5, pp. 1610-1630, May 2005.

where no reference is made to the following prior publication on this Cramer-Rao Lower Bound topic:

Kerr, T. H., “Status of CR-Like Lower bounds for Nonlinear Filtering,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-25, No. 5, pp. 590-601, September 1989 (Author’s reply in Vol. AES-26, No. 5, pp. 896-898, September 1990).

yet several of the references cited in the above papers by Stephen Smith (of the Lincoln Laboratory of MIT) do, in fact, reference the above Kerr article as a significant historical precedent in the Cramer-Rao Lower Bound topic area that was published in a different IEEE Journal even though Kerr was in fact an employee of Lincoln Laboratory when his paper was published but is no longer (for good reasons such as this).  Substantiation of its significance may be found on page 9 in: Branko Ristic, “Cramer Rao Bounds for Target Tracking,” International Conference on Sensor Networks and Information Processing, 6 Dec. 2005.

No there is not “a new sheriff in town” since THK III has pretty much been here and on station all along with eternal vigilance. “Making his list and checking it twice---trying to find out who’s naughty or nice....”
Click here to view our recent short comment submitted to the Institute of Navigation for publication in their Journal. Kerr, T. H., “Comment on 'Low-Noise Linear Combination of Triple-Frequency Carrier Phase Measurements',” Navigation: Journal of the Institute of Navigation, Vol.57, No. 2, pp. 161,162, Summer 2010.
Kerr, T. H., “Comment on ‘Precision Free-Inertial Navigation with Gravity Compensation by an Onboard Gradiometer’,”  AIAA Journal of Guidance, Control, and Dynamics, July-Aug. 2007.
Kerr, T. H., “Comments on ‘Determining if Two Solid Ellipsoids Intersect’,” AIAA Journal of Guidance, Control, and Dynamics, January-February 2005.
Kerr, T. H., “Further Critical Perspectives on Certain Aspects of GPS Development and Use,” Proceedings of 57th Annual Meeting of the Institute of Navigation, 9-13 June 2001.
Kerr, T. H., “Sensor Scheduling in Kalman Filters: Evaluating a Procedure for Varying Submarine Navaids,” Proceedings of 57th Annual Meeting of the Institute of Navigation, 9-13 June 2001.
Kerr, T. H., “Vulnerability of Recent GPS Adaptive Antenna Processing (and all STAP\SLC) to Statistically Non-Stationary Jammer Threats,” Proceedings of SPIE, Session 4473: Tracking Small Targets, 29 July-3 August 2001.
Kerr, T. H., “Exact Methodology for Testing Linear System Software Using Idempotent Matrices and Other Closed-Form Analytic Results,” Proceedings of SPIE, Session 4473: Tracking Small Targets, 29 July-3 August 2001. (closed-form analytic solutions and IMM critique near the end)
Kerr, T. H., “New Lamps for Old: a shell game for generalized likelihood ratio use in radar? Or this isn’t your father’s GLR!,” Proceedings of SPIE, Session 4473: Tracking Small Targets, 29 July-3 August 2001.
Kerr, T. H., “TeK Associates’ view in comparing use of a recursive Extended Kalman Filter (EKF) versus use of Batch Least Squares (BLS) algorithm for UEWR,” TeK Associates, Lexington, MA, (for Raytheon, Sudbury, MA), 12 Sep. 2000.
Kerr, T. H., “Considerations in whether to use Marquardt Nonlinear Least Squares vs. Lambert Algorithm for NMD Cue Track Initiation (TI) Calculations,” TeK Associates Technical Report No. 2000-101, Lexington, MA, (for Raytheon, Sudbury, MA), 27 Sep. 2000.
Kerr, T. H., “Critique of Some Neural Network Architectures and Claims for Control and Estimation,” IEEE Transactions on Aerospace and Electronic Systems, April 1998.
Kerr, T. H., “Comments on ‘An Algorithm for Real-Time Failure Detection in Kalman Filters’,” IEEE Trans. on Automatic Control, May 1998.
Kerr, T. H., “A Critical Perspective on Some Aspects of GPS Development and Use,” Proceedings of 16th Digital Avionics System Conference, Vol. II, pp. 9.4-9 to 9.4-20, Irvine, CA, 26-30 Oct. 1997.  [all worries expressed here by the author regarding GPS vulnerabilities were confirmed in experience in Three W. Mark Barnes, "Artillery Surveyors: Nomads of the Battlefield," Field Artillery, A Professional Bulletin for Redlegs, HQDA P B6-01-1, pp.43-47, Jan.-Feb. 2001]
Kerr, T. H., “Extending Decentralized Kalman Filtering (KF) to 2D for Real-Time Multisensor Image Fusion and\or Restoration: Optimality of Some Decentralized KF Architectures,” Proceedings of the International Conference on Signal Processing Applications & Technology (ICSPAT96), 7-10 October 1996.
Kerr, T. H., “Assessing and Improving the Status of Existing Angle-Only Tracking (AOT) Results,” Proceedings of the International Conference on Signal Processing Applications & Technology (ICSPAT), 24-26 October 1995.
Kerr, T. H., “Use of GPS\INS in the Design of Airborne Multisensor Data Collection Missions (for Tuning NN-based ATR algorithms),” Institute of Navigation Proceedings of GPS-94, 20-23 Sept. 1994.
Kerr, T. H., “Emulating Random Process Target Statistics (using MSF),” IEEE Transactions on Aerospace and Electronic Systems, Vol. 30, No. 2, pp. 556-577, April 1994. (closed-form analytic solutions and critique in Appendix)
Kerr, T. H., “Streamlining Measurement Iteration for EKF Target Tracking,” IEEE Transactions on Aerospace and Electronic Systems, March 1991.
Kerr, T. H., “An Invalid Norm Appearing in Control and Estimation,” IEEE Transactions on Automatic Control, Vol. 23, No. 1, Feb. 1978.  (counterexamples and a correction)
Kerr, T. H., “Testing Matrices for Definiteness and Application Examples that Spawn the Need,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 10, No. 5, pp. 503-506, Sept.-Oct., 1987. 
Kerr, T. H., “Rationale for Monte-Carlo Simulator Design to Support Multichannel Spectral Estimation and/or Kalman Filter Performance Testing and Software Validation/Verification Using Closed-Form Test Cases,” MIT Lincoln Laboratory Report No. PA-512, Lexington, MA, 22 December 1989 (BSD). 
Kerr, T. H., “Status of CR-Like Lower bounds for Nonlinear Filtering,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 25, No. 5, pp. 590-601, Sep. 1989. (an expose) 
Kerr, T. H., “On Misstatements of the Test for Positive Semidefinite Matrices,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 13, No. 3, pp. 571-572, May-Jun. 1990. (occurring in Nav & Target Tracking s/w in ‘70’s/’80's)
Kerr, T. H., “Fallacies in Computational Testing of Matrix Positive Definiteness/Semidefiniteness,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 26, No. 2, pp. 415-421, Mar. 1990. [Using counterexamples, he identifies fallacious algorithms that he found to exist in U.S. Navy submarine navigation and sonobuoy operational software that he reviewed in the late 1970's and early 1980's.]
 Kerr, T. H., “Computational Techniques for the Matrix Pseudoinverse in Minimum Variance Reduced-Order Filtering and Control,” in Control and Dynamic Systems-Advances in Theory and Applications, Vol. XXVIII: Advances in Algorithms and computational Techniques for Dynamic Control Systems, Part 1 of 3, C. T. Leondes (Ed.), Academic Press, NY, 1988.
Kerr, T. H., “Decentralized Filtering and Redundancy Management Failure Detection for Multi-Sensor Integrated Navigation Systems,” Proceedings of the National Technical Meeting of the Institute of Navigation (ION), San Diego, CA, 15-17 January 1985. (an expose)
Kerr, T. H., “Decentralized Filtering and Redundancy Management for Multisensor Navigation,” IEEE Trans. on AES, Vol.23, No. 1, pp. 83-119, Jan. 1987. (an expose)
Kerr, T. H., “Examining the Controversy Over the Acceptability of SPRT and GLR Techniques and Other Loose Ends in Failure Detection,” Proceedings of the American Control Conference, San Francisco, CA, 22-24 June 1983.  (an expose)
Kerr, T. H., “Comments on ‘A Chi-Square Test for Fault Detection in Kalman Filters’,” IEEE Transactions on AC, Vol. 35, No. 11, pp. 1277-1278, November 1990.
Kerr, T. H., “A Critique of Several Failure Detection Approaches for Navigation Systems,” IEEE Transactions on AC, Vol. 34, No. 7, pp. 791-792, July 1989.
Kerr, T.H., and Chin, L., “The Theory and Techniques of Discrete-Time Decentralized Filters,” in Advances in the Techniques and Technology in the Application of Nonlinear Filters and Kalman Filters, edited by C.T. Leondes, AGARDograph No. 256, Noordhoff International Publishing, Lieden, 1981.
Kerr, T. H., “The Proper Computation of the Matrix Pseudo-Inverse and its Impact in MVRO Filtering,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 21, No. 5, Sep. 1985.
Kerr, T. H., “The Principal Minor Test for Semidefinite Matrices-Author’s Reply,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 13, No. 3, p. 767, Sep.-Oct. 1989.
Kerr, T. H., “Three Important Matrix Inequalities Currently Impacting Control and Estimation Applications,” IEEE Transactions on Automatic Control, Vol. AC-23, No. 6, December 1978.
Kerr, T. H., “Functional and Mathematical Structural Analysis of the Passive Tracking Algorithm (PTA),” Intermetrics Report No. IR-MA-208, Cambridge, MA, 25 May 1983, for NADC.
Kerr, T. H., “Comments on ‘Estimation Using a Multirate Filter’,” IEEE Transactions on Automatic Control, Vol. AC-34, No. 3, p. 384, March 1989.
Kerr, T. H., “Comments on ‘Federated Square Root Filter for Decentralized Parallel Processes’,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-27, No. 6, November 1991.   Go to Top

Explanations pop-up instantaneously where you need them but only when requested, as seen below for the single button appearing on the screen above. An exception is if the USER sets Prompters_On as an option that can be activated from the Menu Bar appearing on most of the primary Screens. When Prompters_On is set, many of the informational screens open automatically when that screen is visited as a helpful mnemonic device. This feature is especially useful when a substantial period of time elapses between TK-MIP activation as other tasks are being pursued. No user manual is ever necessary to feel comfortable and confident in running TK-MIP. This prompting does not make use of the Internet. Otherwise TK-MIP could not be run in a secure stand-alone CLASSIFIED mode.

The close (equivalent) model relationship between a Box-Jenkins time-series representation and a state variable representation has been known for a least  4 or 5 decades, as spelled out in:  A. Gelb (Ed.), “Applied Optimal Estimation,” MIT Press, Cambridge, MA, 1974.
Kerr, T. H., “Applying Stochastic Integral Equations to Solve a Particular Stochastic Modeling Problem,” Ph.D. Thesis in the Department of Electrical Engineering, University of Iowa, Iowa City, Iowa, January 1971. (This offers a simple algorithm for easily converting an ARMA time-series into a more tractable AR one of higher dimension.)
Kerr, T. H., Multichannel Shaping Filter Formulations for Vector Random Process Modeling Using Matrix Spectral Factorization, MIT Lincoln Laboratory Report No. PA-500, Lexington, MA, 27 March 1989. (This offers a simple algorithm for easily converting an ARMA time-series into a more tractable AR one of higher dimension.)
Kerr, T. H., “Emulating Random Process Target Statistics (Using MSF),” IEEE Trans. on Aerospace and Electronic Systems, Vol. 30, No. 2, pp. 556-577, Apr. 1994. (This offers a simple algorithm for easily converting an ARMA time-series into a more tractable AR one of higher dimension.)

Please click on http://filext.com/file-extension/TEK for free ways to check your Window's registry for compatibility with TK-MIP and its ability to automatically access the various file extensions that it needs to access (as representatively sampled in the file view above) in order that TK-MIP work properly without conflict after it is installed.

Please click on http://filext.com/file-extension/TEK for free ways to check your Window's registry for compatibility with TK-MIP and its ability to automatically access the various file extensions that it needs to access (as representatively sampled in the file view above) in order that TK-MIP work properly without conflict after it is installed.

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Sh, Tom sees moths. 

Are we not drawn onward to new era?

To Idi Amin. I'm a idiot.

Splat! I hit Alps.

Norma is as selfless as I am, Ron.

Click here to view more of the beauty of Arithmetic rather than of Mathematics, as claimed.

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TeK Associates’ motto : “We work hard to make your job easier!”