66,565 research outputs found
Welch Planning Mill, P.1
No full text31522 Welch Planing Mill, 375 No. Main Street, Midvale, Nov. 7, 1957. Shipler Comm. Photog. #7104
p-adic Welch Bounds and p-adic Zauner Conjecture
No full textLet be a prime. For , let be the standard -dimensional p-adic Hilbert space. Let and be the p-adic Hilbert space of symmetric m-tensors. We prove the following result. Let be a collection in satisfying (i) for all and (ii) there exists satisfying for all Then
\begin{align}\label{WELCHNONABSTRACT}
\max_{1\leq j,k \leq n, j \neq k}\{|n|, |\langle \tau_j, \tau_k\rangle|^{2m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }.
\end{align}
We call Inequality (\ref{WELCHNONABSTRACT}) as the p-adic version of Welch bounds obtained by Welch [\textit{IEEE Transactions on Information Theory, 1974}]. Inequality (\ref{WELCHNONABSTRACT}) differs from the non-Archimedean Welch bound obtained recently by M. Krishna as one can not derive one from another. We formulate p-adic Zauner conjecture
p-adic Welch Bounds and p-adic Zauner Conjecture
No full textLet be a prime. For , let be the standard -dimensional p-adic Hilbert space. Let and be the p-adic Hilbert space of symmetric m-tensors. We prove the following result. Let be a collection in satisfying (i) for all and (ii) there exists satisfying for all Then
\begin{align}
(1) \quad \quad \quad \max_{1\leq j,k \leq n, j \neq k}\{|n|, |\langle τ_j, τ_k\rangle|^{2m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (1) as the p-adic version of Welch bounds obtained by Welch [\textit{IEEE Transactions on Information Theory, 1974}]. Inequality (1) differs from the non-Archimedean Welch bound obtained recently by M. Krishna as one can not derive one from another. We formulate p-adic Zauner conjecture.10 Pages, 0 Figure
It happens every night
No full textGift of Dr. Mary Jane Esplen.Piano vocal [instrumentation]A boy met a girl [first line]But it happens ev'ry night [first line of chorus]G [key]Tempo di valse [tempo]Popular song [form/genre]Couple table trees ; Emmett J. Welch and his Merry Minstrels (photograph) [illustration]Publisher's advertisement on inside front and back cover [note
Measurement of the ratio of prompt χ c to J / ψ production in pp collisions at √s = 7 TeV
No full textThe prompt production of charmonium χ c and J / ψ states is studied in proton-proton collisions at a centre-of-mass energy of √s = 7 TeV at the Large Hadron Collider. The χ c and J / ψ mesons are identified through their decays χ c → J / ψ γ and J / ψ → μ + μ - using 36 pb - 1 of data collected by the LHCb detector in 2010. The ratio of the prompt production cross-sections for χ c and J / ψ, σ (χ c → J / ψ γ) / σ (J / ψ), is determined as a function of the J / ψ transverse momentum in the range 2 < p T J / ψ < 15 GeV / c. The results are in excellent agreement with next-to-leading order non-relativistic expectations and show a significant discrepancy compared with the colour singlet model prediction at leading order, especially in the low p T J / ψ region
Non-Archimedean and p-adic Functional Welch Bounds
No full textWe prove the non-Archimedean (resp. p-adic) Banach space version of non-Archimedean (resp. p-adic) Welch bounds recently obtained by M. Krishna. More precisely, we prove following results.
\begin{enumerate}[\upshape(i)]
\item Let be a non-Archimedean (complete) valued field satisfying for all , for all Let be a -dimensional non-Archimedean Banach space over . If is any collection in and is any collection in (dual of )
satisfying for all and the operator , is diagonalizable, then
\begin{align}\label{NONFUNCTIONALWELCH}
\max_{1\leq j,k \leq n, j \neq k}\{|n|, |f_j(\tau_k)f_k(\tau_j)|^{m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }.
\end{align}
We call Inequality (\ref{NONFUNCTIONALWELCH}) as non-Archimedean functional Welch bounds.
\item For a prime , let be the p-adic number field. Let be a -dimensional p-adic Banach space over . If is any collection in and is any collection in (dual of ) satisfying for all and there exists such that for all then
\begin{align}\label{PADICFUNCTIONALWELCH}
\max_{1\leq j,k \leq n, j \neq k}\{|n|, |f_j(\tau_k)f_k(\tau_j)|^{m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }.
\end{align}
We call Inequality (\ref{PADICFUNCTIONALWELCH}) as p-adic functional Welch bounds.
\end{enumerate}
We formulate non-Archimedean functional and p-adic functional Zauner conjectures
Letter from Carl Hayden to P. J Moran
No full textLetter from Carl T. Hayden to P. J. Moran concerning the alignment of the road to Bright Angel Trail
Letter from P. J. Moran to Carl Hayden
No full textLetter from P. J. Moran to Carl T. Hayden inquiring when construction will begin on the approach road to Bright Angel Trail
Letter from P. J. Moran to Carl Hayden
No full textLetter from P. J. Moran to Carl T. Hayden inquiring when construction will begin on the approach road to Bright Angel Trai
Telegrams Between Carl Hayden to P. J. Moran, Democratic County Central Committee
No full textTelegram from Carl Hayden to P. J. Moran regarding the resignation of W. W. Crosby and his replacement J. R. Eakin
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