178,498 research outputs found
Further refinements of the Heinz inequality
The celebrated Heinz inequality asserts that for , A,B\in \+, every unitarily invariant norm
and . In this paper, we present several
improvement of the Heinz inequality by using the convexity of the function
, some integration techniques
and various refinements of the Hermite--Hadamard inequality. In the setting of
matrices we prove that \begin{eqnarray*}
&&\hspace{-0.5cm}\left|\left|\left|A^{\frac{\alpha+\beta}{2}}XB^{1-\frac{\alpha+\beta}{2}}+A^{1-\frac{\alpha+\beta}{2}}XB^{\frac{\alpha+\beta}{2}}\right|\right|\right|\leq\frac{1}{|\beta-\alpha|}
\left|\left|\left|\int_{\alpha}^{\beta}\left(A^{\nu}XB^{1-\nu}+A^{1-\nu}XB^{\nu}\right)d\nu\right|\right|\right|\nonumber\\
&&\qquad\qquad\leq
\frac{1}{2}\left|\left|\left|A^{\alpha}XB^{1-\alpha}+A^{1-\alpha}XB^{\alpha}+A^{\beta}XB^{1-\beta}+A^{1-\beta}XB^{\beta}\right|\right|\right|\,,
\end{eqnarray*} for real numbers .Comment: 15 pages, to appear in Linear Algebra Appl. (LAA
Properties of chains of prime ideals in an amalgamated algebra along an ideal
Let be a ring homomorphism and let be an ideal of . In
this paper, we study the amalgamation of with along with respect to
(denoted by ), a construction that provides a general frame
for studying the amalgamated duplication of a ring along an ideal, introduced
and studied by D'Anna and Fontana in 2007, and other classical constructions
(such as the , the and the constructions). In
particular, we completely describe the prime spectrum of the amalgamated
duplication and we give bounds for its Krull dimension.Comment: J. Pure Appl. Algebra (to appear
On Minimizing ||S−(AX−XB)||Pp
In this paper, we minimize the map Fp (X)= ||S−(AX−XB)||Pp ,
where the pair (A, B) has the property (F P )Cp , S ∈ Cp , X varies such that
AX − XB ∈ Cp and Cp denotes the von Neumann-Schatten class
Measured Sonic Boom Signatures Above and Below the XB-70 Airplane Flying at Mach 1.5 and 37,000 Feet
During the 1966-67 Edwards Air Force Base (EAFB) National Sonic Boom Evaluation Program, a series of in-flight flow-field measurements were made above and below the USAF XB-70 using an instrumented NASA F-104 aircraft with a specially designed nose probe. These were accomplished in the three XB-70 flights at about Mach 1.5 at about 37,000 ft. and gross weights of about 350,000 lbs. Six supersonic passes with the F-104 probe aircraft were made through the XB-70 shock flow-field; one above and five below the XB-70. Separation distances ranged from about 3000 ft. above and 7000 ft. to the side of the XB-70 and about 2000 ft. and 5000 ft. below the XB-70. Complex near-field "sawtooth-type" signatures were observed in all cases. At ground level, the XB-70 shock waves had not coalesced into the two-shock classical sonic boom N-wave signature, but contained three shocks. Included in this report is a description of the generating and probe airplanes, the in-flight and ground pressure measuring instrumentation, the flight test procedure and aircraft positioning, surface and upper air weather observations, and the six in-flight pressure signatures from the three flights
Vertical versus horizontal Poincar\'e inequalities on the Heisenberg group
Let be the discrete
Heisenberg group, equipped with the left-invariant word metric
associated to the generating set .
Letting B_n= {x\in \H: d_W(x,e_\H)\le n} denote the corresponding closed ball
of radius , and writing , we prove that if
is a Banach space whose modulus of uniform convexity has power
type then there exists such that every
satisfies {multline*} \sum_{k=1}^{n^2}\sum_{x\in
B_n}\frac{|f(xc^k)-f(x)|_X^q}{k^{1+q/2}}\le K\sum_{x\in B_{21n}}
\Big(|f(xa)-f(x)|^q_X+\|f(xb)-f(x)\|^q_X\Big). {multline*} It follows that for
every the bi-Lipschitz distortion of every is at least a
constant multiple of , an asymptotically optimal estimate as
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