Estimations of optimum plot size using data from Bromegrass uniformity trials

Uniformity data from three fields of Fischer bromegrass, one planted in rows 31/2 feet apart and the others broadcast, were analyzed to obtain estimates of optimum size and shape of plot for use in field experimentation. Forage yields were taken on 1,296 unit plots, 31/2 X 4 feet, in each field and added together in various combinations to give different sizes and shapes of plots. Comparable variances and variances per basic unit for each plot size were then obtained by dividing between-plot variances by the number of units per plot and the square of the number of units per plot, respectively. Dry matter percentages of samples ranged from 35.2 to 40.6 percent in the row-planting and from 32.8 to 41.5 percent in the broadcast planting in 1950. Means were 37.6 and 38.0 percent, respectively. Analyses of variance indicated that differences in dry matter percentages due to location within fields were not significant

Sudangrass in Iowa

In Iowa sudangrass is an outstanding temporary pasture crop during the summer months of July, August and September. It can also be used for emergency hay or silage. Here are some tips on varieties and management

Orchardgrass -- Its Use on Iowa Farms

The true value of orchardgrass has only recently been realized in the north-central states. Experiment stations in this area are now, however, aware of its possibilities and are conducting extensive studies on use, management and improvement. Results have shown many features which place orchardgrass among the best grasses now available. Some of these features are

Grain Sorghum - A Coming Crop in Iowa?

It looks as though grain sorghum will grow and produce satisfactorily in some parts of the state- particularly in the southern and western parts. But it may not do as well as corn in the male corn-producing areas

Duals of variable exponent Hörmander spaces (0<p−≤p+≤10< p^- \le p^+ \le 1) and some applications

In this paper we characterize the dual \bigl(\B^c_{p(\cdot)} (\Omega) \bigr)' of the variable exponent H\"or\-man\-der space \B^c_{p(\cdot)} (\Omega) when the exponent $p(\cdot)$ satisfies the conditions $0 < p^- \le p^+ \le 1$, the Hardy-Littlewood maximal operator $M$ is bounded on $L_{p(\cdot)/p_0}$ for some $0 < p_0 < p^-$ and $\Omega$ is an open set in $\R^n$. It is shown that the dual \bigl(\B^c_{p(\cdot)} (\Omega) \bigr)' is isomorphic to the H\"ormander space \B^{\mathrm{loc}}_\infty (\Omega) (this is the $p^+ \le 1$ counterpart of the isomorphism \bigl(\B^c_{p(\cdot)} (\Omega) \bigr)' \simeq \B^{\mathrm{loc}}_{\widetilde{p'(\cdot)}} (\Omega), $1 < p^- \le p^+ < \infty$, recently proved by the authors) and hence the representation theorem \bigl( \B^c_{p(\cdot)} (\Omega) \bigr)' \simeq l^{\N}_\infty is obtained. Our proof relies heavily on the properties of the Banach envelopes of the steps of \B^c_{p(\cdot)} (\Omega) and on the extrapolation theorems in the variable Lebesgue spaces of entire analytic functions obtained in a precedent paper. Other results for $p(\cdot) \equiv p$, $0 < p < 1$, are also given (e.g. \B^c_p (\Omega) does not contain any infinite-dimensional $q$-Banach subspace with $p < q \le 1$ or the quasi-Banach space \B_p \cap \E'(Q) contains a copy of $l_p$ when $Q$ is a cube in $\R^n$). Finally, a question on complex interpolation (in the sense of Kalton) of variable exponent H\"ormander spaces is proposed.J. Motos is partially supported by grant MTM2011-23164 from the Spanish Ministry of Science and Innovation. The authors wish to thank the referees for the careful reading of the manuscript and for many helpful suggestions and remarks that improved the exposition. In particular, the remark immediately following Theorem 2.1 and the Question 2 were motivated by the comments of one of them.Motos Izquierdo, J.; Planells Gilabert, MJ.; Talavera Usano, CF. (2015). Duals of variable exponent Hörmander spaces ($0< p^- \le p^+ \le 1$) and some applications. Revista- Real Academia de Ciencias Exactas Fisicas Y Naturales Serie a Matematicas. 109(2):657-668. https://doi.org/10.1007/s13398-014-0209-zS6576681092Aboulaich, R., Meskine, D., Souissi, A.: New diffussion models in image processing. Comput. Math. Appl. 56(4), 874–882 (2008)Acerbi, E., Mingione, G.: Regularity results for stationary electro-rheological fluids. Arch. Ration. Mech. Anal. 164(3), 213–259 (2002)Bastero, J.: $$l^q$$ l q -subspaces of stable $$p$$ p -Banach spaces, $$0 < p \le 1$$ 0 < p ≤ 1 . Arch. Math. (Basel) 40, 538–544 (1983)Boas, R.P.: Entire functions. Academic Press, London (1954)Boza, S.: Espacios de Hardy discretos y acotación de operadores. Dissertation, Universitat de Barcelona (1998)Cruz-Uribe, D., Fiorenza, A.: Variable Lebesgue spaces, foundations and harmonic analysis. Birkhäuser, Basel (2013)Cruz-Uribe, D.: SFO, A. Fiorenza, J. M. Martell, C. Pérez: The boundedness of classical operators on variable $$L^p$$ L p spaces. Ann. Acad. Sci. Fenn. Math. 31, 239–264 (2006)Diening, L., Harjulehto, P., Hästö, P., Růžička, M.: Lebesgue and sobolev spaces with variable exponents. lecture notes in mathematics, vol. 2007. Springer, Berlin, Heidelberg (2011)Hörmander, L.: The analysis of linear partial operators II, Grundlehren 257. Springer, Berlin, Heidelberg (1983)Hörmander, L.: The analysis of linear partial operators I, Grundlehren 256. Springer, Berlin, Heidelberg (1983)Kalton, N.J., Peck, N.T., Roberts, J.W.: An $$F$$ F -space sampler, London Mathematical Society Lecture Notes, vol. 89. Cambridge University Press, Cambridge (1985)Kalton, N.J.: Banach envelopes of non-locally convex spaces. Canad. J. Math. 38(1), 65–86 (1986)Kalton, N.J., Mitrea, M.: Stability results on interpolation scales of quasi-Banach spaces and applications. Trans. Am. Math. Soc. 350(10), 3903–3922 (1998)Kalton, N.J.: Quasi-Banach spaces, Handbook of the Geometry of Banach Spaces, vol. 2. In: Johnson, W.B., Lindenstrauss, J. (eds.), pp. 1099–1130. Elsevier, Amsterdam (2003)Köthe, G.: Topological vector spaces I. Springer, Berlin, Heidelberg (1969)Motos, J., Planells, M.J., Talavera, C.F.: On variable exponent Lebesgue spaces of entire analytic functions. J. Math. Anal. Appl. 388, 775–787 (2012)Motos, J., Planells, M.J., Talavera, C.F.: A note on variable exponent Hörmander spaces. Mediterr. J. Math. 10, 1419–1434 (2013)Stiles, W.J.: Some properties of $$l_p$$ l p , $$0 < p < 1$$ 0 < p < 1 . Studia Math. 42, 109–119 (1972)Triebel, H.: Theory of function spaces. Birkhäuser, Basel (1983)Vogt, D.: Sequence space representations of spaces of test functions and distributions. In: Zapata, G.I. (ed.) Functional analysis, holomorphy and approximation theory, Lecture Notes in Pure and Applied Mathematics, vol. 83, pp. 405–443 (1983

Reflexive representability and stable metrics

It is well-known that a topological group can be represented as a group of isometries of a reflexive Banach space if and only if its topology is induced by weakly almost periodic functions (see \cite{Shtern:CompactSemitopologicalSemigroups}, \cite{Megrelishvili:OperatorTopologies} and \cite{Megrelishvili:TopologicalTransformations}). We show that for a metrisable group this is equivalent to the property that its metric is uniformly equivalent to a stable metric in the sense of Krivine and Maurey (see \cite{Krivine-Maurey:EspacesDeBanachStables}). This result is used to give a partial negative answer to a problem of Megrelishvili

Nonlinear spectral calculus and super-expanders

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively under zigzag products. These results yield a combinatorial construction of super-expanders, i.e., a sequence of 3-regular graphs that does not admit a coarse embedding into any uniformly convex normed space.Comment: Typos fixed based on referee comments. Some of the results of this paper were announced in arXiv:0910.2041. The corresponding parts of arXiv:0910.2041 are subsumed by the current pape