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INTEGRATION OF PATHS—A FAITHFUL REPRE- SENTATION OF PATHS BY NONCOMMUTATIVE FORMAL POWER SERIES BY KUO-TSAI CHEN In the m-dimensional affine space ” with the coordinates (x;, - - - , Xm), the product a ... A path a in M is a map a: [a, b]—>M which is Presented to the Society on April 21, 1956 under the title Integration of paths—A unique — of paths by noncommutative formal power series; received by the editors ...
To say the least, this is not a book for the mathematically faint of heart. ... The Mathematics of Syntactic Structure is, nevertheless, a faithful representation of the state of the art in this area, and can be recommended as a useful primer for com- putational linguists on descriptive ...
A path integral formula for polar coordinates is also discussed, to be understood as a faithful representation of the Schrédinger equation.” ... Summary: “We discuss the canonical and path integral quantisa- tion of a particle moving on a curved manifold. We advance a simple prescription to quantise the system within the canonical formalism. ...
Philosophy of Science
NUMEROSITY, NUMBER, ARITHMETIZATION, MEASUREMENT AND PSYCHOLOGY 187 arbitrary interpretation when explanation of a behavior of a biological organism is at issue, formal operations faithful to natural processes ... Ascertaining enough about K and L to fix the limits of significant mathematical transformation.” Formal operations and psychological theory. ...
This may be a result of the economy of his style, or evidence of a flattering faith in the sophistication of his readers. ... Lewin’s topological psychology may be viewed as an em- pirical interpretation of the already developed formal system of mathematical topology (or a sub-system of this). ...
By means of the test the author hopes to show that the new formal theory is “in some sense a faithful rendering” of Russell’s own thought. ... The author tests the formalization by using it to symbolically reconstruct one of Russell’s arguments in Section 500 of Principles of mathematics [op. cit.]. ...
The L(/,m;n) are determined up to isomorphism by their formal characters. Let h be a Cartan subalgebra of g and @ be the highest weight of V with respect to g. ... In this paper, the author constructs a subcrystal of Littelmann’s path crystal whose formal character coincides with that of a certain simple integral module of level zero over the affine Lie algebra sl ...
A few changes have been made, largely in the form of amplifications, but the result is faithful to what was delivered there. ... The author discusses two somewhat different topics: the quantum theory of (continuous) measurement, and gauge theory and grav- itation, using as a unifying theme the so-called “path formalism” , in particular ...
504 THE MATHEMATICS TEACHER bundles in the teacher’s mind and in the student’s mind we get some idea of how weak this thing that we call a complete proof is to the student. ... We have faith in logic because we have tested it by experience, not simply because it is logic. We expect a logical proof to carry the same conviec- tion to a student as it does to us. It cannot. ...
The answer is, it walks the path of God Himself Not blinded by a faith. It knows—it is divine. BOOK NOTICES. S. C. ... The proposition is not why is man in possession of a faculty quickly to grasp and apply the proposi- tion of one plus one being two, or why does he easily acquire arithmetic and mathematics? ...
Incompleteness limits the detectability of machine consciousness. This is an effort to convey these thoughts and results in a somewhat entertaining manner. ... Incompleteness limits our ability to ever understand every observable phenomenon in the universe. Incompleteness limits the ability of evolutionary processes from finding optimal solutions. ... Rather, it requires faith to believe that this is how they all came to be. Belief in Dawkin's "Blind Watchmaker" requires blind faith. ...arXiv:1602.07646v2 fatcat:bkdqgbgrejdaxbbnn7wx7jtzhm
The Journal of Applied Ecology
enables faith¬ ful representation of the paths of the animals. ... A formal comparison of observed and predicted trajectories is very difficult and one usually relies on summary statistics to do so. ...
Following a theoretical dissection of possible user interaction with these mathematical simulations, we categorize them in relation to other environments supporting the construction of mathematical proofs ... along the dimensions of "interactivity" and "formality." ... Formality Formality describes the adherence to standardized mathematical notation in the representation of mathematics, which is distinct from "formal," meaning written in a formalized language with formalized ...doi:10.1007/s40753-020-00125-6 fatcat:doudxkmt4nerzeftrov7m366b4
A way to begin is hierarchical simulation. Coexistent interdependent hierarchical types of different kinds structure the universe of models for complex systems. ... Simulation of conscience demands transcending from computability to simulability by an intensive effort on extensive research to integrate essential mathematical and physical knowledge guided by philosophical ... We have to build a metric space where knowledge ° construction is a contraction, i.e., elements implied in the construction get closer to one another in the formal understanding of the formal construct ...doi:10.1080/02286203.2004.11442284 fatcat:jfiv7fht3fhqxnfpxeiei4lgtu
This is a short tribute to Aleksandr A. Borovkov on the occasion of his 80th birthday. ... For over half a century Borovkov is one of the best sherpas on the tortuous path to the new frontiers of scientific thought. Borovkov is a heir of the legacy of the Moscow mathematical school. ... Unfortunately, there are much more ways to betray truth than the paths leading to it. To be a scientist by belief is a state not certified, not compulsory, and rather rare for a man of science. ...doi:10.1134/s003744661104001x fatcat:t2fmmroawfhb7oqjmuutrk3i4q
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