Some counterpart inequalities for a functional associated with Jensen's inequality.

Dragomir, Sever Silvestru; Goh, C.J.

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A refinement of an inequality from information theory.

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Conditions for periodic vibrations in a symmetric n-string

Claude Gauthier (2008)

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A symmetric N-string is a network of N ≥ 2 sections of string tied together at one common mobile extremity. In their equilibrium position, the sections of string form N angles of 2π/N at their junction point. Considering the initial and boundary value problem for small-amplitude oscillations perpendicular to the plane of the N-string at rest, we obtain conditions under which the solution will be periodic with an integral period.

Diassociativity is not finitely based relative to power associativity

Tomasz Kowalski (2010)

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Vito Lampret (2012)

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An asymptotic approximation of Wallis’ sequence W(n) = Πk=1n 4k 2/(4k 2 − 1) obtained on the base of Stirling’s factorial formula is presented. As a consequence, several accurate new estimates of Wallis’ ratios w(n) = Πk=1n(2k−1)/(2k) are given. Also, an asymptotic approximation of π in terms of Wallis’ sequence W(n) is obtained, together with several double inequalities such as, for example, $W (n) \cdot (a_{n} + b_{n}) < π < W (n) \cdot (a_{n} + b_{n}^{'})$ with $a_{n} = 2 + \frac{1}{2 n + 1} + \frac{2}{3 {(2 n + 1)}^{2}} - \frac{1}{3 n {(2 n + 1)}^{'}} b_{n} = \frac{2}{33 {(n + 1)}^{2^{'}}} b_{n}^{'} \frac{1}{13 n^{2^{'}}} n \in ℕ$ .

Invariant subspaces for polynomially compact almost superdiagonal operators on $l (p_{i})$ .

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Differential geometry of grassmannians and the Plücker map

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Using the Plücker map between grassmannians, we study basic aspects of classic grassmannian geometries. For ‘hyperbolic’ grassmannian geometries, we prove some facts (for instance, that the Plücker map is a minimal isometric embedding) that were previously known in the ‘elliptic’ case.