Type Systems - Science topic

I just encountered a notification about this article on Mathematical Proofs and the value of Proof Assistants, https://www.ams.org/journals/notices/202401/rnoti-p79.pdf

I resonate most with the positions by Lamport (author of LaTex and a Turing Award Laureate) and Laurence Paulson (author of ML for the Working Programmer and working very much in proof assistants). I think it will be clear that the situation about the presentation of proofs and incorporation of such proofs in mathematical publication is still very much up in the air.

I also did a ResearchGate search on "Proof Assistant" and the fire-hose of articles confirmed my view that this is yet stabilizing, although there are extensive favorite approaches.

Here is the above paper's abstract:

“A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into peril. Now may be the time to reconcile theory and practice, i.e., precision and intuition, through the advent of computer proof assistants. This used to be a topic for experts in specialized communities. However, mathematical proofs have become increasingly sophisticated, stretching the boundaries of what is humanly comprehensible, so that leading mathematicians have asked for formal verification of their proofs. At the same time, major theorems in mathematics have recently been computer-verified by people from outside of these communities, even by beginning students. This article investigates the different definitions of a proof, the gap between them, and possibilities to build bridges. It is written as a polemic or a collage by different members of the communities in mathematics and computer science at different stages of their careers, challenging well-known preconceptions and exploring new perspectives.”

There is already an objection to this material on the list where I found it. The objection is to this statement: "This puts the unique status of mathematics as exact science into peril.” That statement disturbs me too, but maybe not for the same reason.

Dear Peter!

Sorry! P(z) is the mxm transfer function of some nD Givone-Roesser type system or of some nD Fornasini-Marchesini type system, and z=(z1,z2,...,zn), with n at least 2.

I've already reported that the answer is "no" in general, unless m=1, where the problem is trivial.

But anyway, Many Thanks For Your Interest And Response!

Why do you absolutely want to use sliding modes?

Travis,

This is an interesting question and one that I haven't really seen proposed anywhere. However, it does seem logical that "stream order" could be used to describe road usage, at least to some degree. You might be able to contact the department of transportation in your state and see if they have data on road usage from different "orders". They often collect this type of data when looking at widening roads, adding new stoplights, etc. So, any data they have and can share would allow you to look at possibly providing a proof of concept for this type of system.

Thanks for asking. Actually I am very beginner in image and vedio processing. But I actually want to make such an extension that not only protect porn related searching but also stop this kind of advertisement, also working with youtube, and that can be mantain by parents for childern and device will be save for them. Those which are already introduced work only to protect from searching which I have seen. So I think this will be a devolapment of this kind of software.

You are welcome.

This scenario has many critical measures and effect keeping usability and risk mitigation in mind. There are different types of farming, e.g. limited time serial farming where adult plants can be planted to harvest fresh and with quality like flowers, that needs prediction for month. similarly there are many use cases in this domain.

Thanks all, sharing DICOM systems definitely differ a lot in various countries! That is why I want to get as much info as possible...

Both the systems are good for bacterial identification even if the Vitek system is better especially for environmental species; moreover you have to consider the cost that for ViteK is much higher than for the API system.

what is the approximate difference of conductance values between the two different data sets. if the difference is small and the cmc values are similar then you can take average of different data sets.

usually we keep concentration of one surfactant fixed and titrate it with other surfactant ( micellar range ).

Usually CMC of such systems does not show any regular pattern but the conductance values are usually similar

Single-Degree-of-Freedom (SDOF) electromagnetic generator model probably suitable for this purpose.

Hi dear,

Thanks for the question.

The best absorber for ammonia is water. The Oldham's diagram is useful for this purpose (ammonia in cooling devices).

with my best wishes.

Adel OUESLATI

see lots of examples: http://spinroot.com/cobra/papers

It is very hard to require among several zeros every zero be LHP. Therefore most of systems are non-minimum phase, and this proposed question is very important.

From root locus rules, the most obvious harm of RHL zeros is that high gain is prohibited, because high gain can make the closed poles reach these zeros.

This is why the asymptotic LTR of state space theory cannot be applied to non-minimum phase systems, because asymptotic LTR means asymptotic high gains.

However, using a simple state space technique described in my publications, an output feedback compensator (OFC) can be designed for systems either with more outputs than inputs or with at least one LHP zeros (the OFC poles will be assigned to match these LHP zeros).

This OFC is very general because it is equally very hard to have among several zeros every zero be RHP.

This OFC can estimate a number of linear transformations of system state (like a number of additional system outputs), while this number equals the OFC order. Thus a much improved static output feedback control can be designed. This form of control is a constrained state feedback control, which is by far the best form of feedback control.

This OFC has a distinct advantage than normal observers. The exact LTR or full realization of robustness of state feedback control, is achieved by OFC.

This OFC fully utilizes the LHP zeros by matching them with the OFC poles, while avoiding the harms of RHP zeros by not requiring high gains at all.

Your system is not smooth enough for backstepping design if you want to stabilize the system to the origin.  But, due to the structure of the system may exist if one considers only 0 \leq h_2 \leq h_1 region in the state space.  (The system is only well defined in that region.)  Now, change the coordinates to (x_1,x_2) = (h_2,h_1 - h_2) and use x_1 as the output, q as the input, and x_2 as the virtual control input.  Remember that x_1 and x_2 are both nonnegative and you don't have full control authority in the stabilization of x_1 dynamics.  But, x_1 will go to zero if x_2 is zero.  So, set the virtual control law x_2 = 0 and continue to the second step of backstepping, where you have full control authority with input q.  Try this to see the result.  

Dear Dr. Tina,

i've been working for a system integrator company in the central east coast of italy. We developed a solution for a PVT panel and i tried to model and control the prototype.

I used a non linear economic target function and an heuristic optimization (hill climbing method with fuzzy logic)

attached a preliminary version of the paper published in the IECON 2013 proceedings...

i hope it will be useful...

best regards

Lucio