Boosting Beta-Cell Numbers

Quantitative Assessment of Proliferative Effects of Oral Vanadium on Pancreatic Islet Volumes and Beta Cell Numbers of Diabetic Rats

Background: Oral vanadyl sulfate (vanadium) induces normoglycemia, proliferates beta cells and prevents pancreatic islet atrophy in streptozotocin-induced diabetic rats. Soteriological method is used to quantitate the proliferative effects of vanadium on beta-cell numbers and islet volumes of normal and diabetic rats. Methods: Adult male Sprague-Dawley rats were made diabetic with intravenous s...

Boosting Local Consistency Algorithms over Floating-Point Numbers

Solving constraints over oating-point numbers is a critical issue in numerous applications notably in program veri cation. Capabilities of ltering algorithms over the oating-point numbers (F) have been so far limited to 2b-consistency and its derivatives. Though safe, such ltering techniques su er from the well known pathological problems of local consistencies, e.g., inability to e ciently han...

beta-EXPANSIONS WITH DELETED DIGITS FOR PISOT NUMBERS beta

Beta-representations of 0 and Pisot numbers

Let β > 1, d a positive integer, and Zβ,d = {z1z2 · · · | ∑ i>1 ziβ −i = 0, zi ∈ {−d, . . . , d}} be the set of infinite words having value 0 in base β on the alphabet {−d, . . . , d}. Based on a recent result of Feng on spectra of numbers, we prove that if the set Zβ,⌈β⌉−1 is recognizable by a finite Büchi automaton then β is a Pisot number. As a consequence of previous results, the set Zβ,d i...

On beta expansions for Pisot numbers

Given a number β > 1, the beta-transformation T = Tβ is defined for x ∈ [0, 1] by Tx := βx (mod 1). The number β is said to be a betanumber if the orbit {Tn(1)} is finite, hence eventually periodic. In this case β is the root of a monic polynomial R(x) with integer coefficients called the characteristic polynomial of β. If P (x) is the minimal polynomial of β, then R(x) = P (x)Q(x) for some pol...