We state two conjectures, which together would yield strong results of algebraic independence related to Schanuel’s Conjecture. Partial results on these conjectures are also discussed. 1991 Mathematics Subject Classification: 11J82, 11J85.

PURPOSE/OBJECTIVES To pilot a second support group intervention study promoting self-transcendence perspectives and activities and to document changes over time in well-being in support group participants compared with nonparticipants. DESIGN Quasiexperimental, partial randomization, preference trial design. SETTING An urban breast cancer resource center established by survivors. SAMPLE 4...

objective: the current study aimed at investigating the role of patience and its components in predicting self-control among high school students in shiraz, iran. methods: the statistical population of the study included all high school students of shiraz. three hundred and thirty-two students (161 females and 171 males) were recruited via cluster sampling method. the subjects participated in t...

In this work, we define the concept of Liouville numbers as well as the standard construction to obtain Liouville numbers and we prove their most important properties: irrationality and transcendence. This is historically interesting since Liouville numbers constructed in the standard way where the first numbers that were proven to be transcendental. The proof is very elementary and requires on...

Let k be an algebraically closed field of characteristic 0 and let D be a division algebra whose center F contains k. We shall say that D can be reduced to r parameters if we can write D ≃ D0 ⊗F 0 F , where D0 is a division algebra, the center F0 of D0 contains k and trdeg k (F0) = r. We show that every division algebra of odd degree n ≥ 5 can be reduced to ≤ 1 2 (n − 1)(n − 2) parameters. More...

It was observed long ago (see e.g., [32] or [20], page 62) that Roth’s theorem [28] and its p-adic extension established by Ridout [27] can be used to prove the transcendence of real numbers whose expansion in some integer base contains repetitive patterns. This was properly written only in 1997, by Ferenczi and Mauduit [21], who adopted a point of view from combinatorics on words before applyi...

Let k be an algebraically closed field of characteristic zero, L its finitely generated extension of transcendence degree ≥ 2, and L another finitely generated extension of k. It is a result of Bogomolov [B2] that any isomorphism between Gal(L/L) and Gal(L′/L) is induced by an isomorphism of fields L −→ L′ identifying L with L. If the transcendence degree of L over k is one, the group Gal(L/L) ...

Let K be a field and v a valuation on K. We discuss some properties of extensions w of v to the field K(X1, . . . , Xn) of rational functions in n variables over K, for which the residue field of w has transcendence degree n over the residue field of v. 2000 Mathematics Subject Classification: 12J20, 12F20. 1.Introduction LetK be a field and v a valuation onK. Residual transcendental extensions...

The authors address the diagnosis problem in nonlinear systems by using the concept of the differential transcendence degree of a differential field extension. The authors also consider the algebraic observability concept of the variable which models the failure presence for the solvability of the diagnosis problem. The construction of a reduced-order uncertainty observer (unknown-input observe...

Is it possible to distinguish algebraic from transcendental real numbers by considering the b-ary expansion in some base b 2? In 1950, É. Borel suggested that the answer is no and that for any real irrational algebraic number x and for any base g 2, the g-ary expansion of x should satisfy some of the laws that are shared by almost all numbers. For instance, the frequency where a given finite se...