Mean-bounded operators and mean ergodic theorems

AbstractIn any reflexive Banach (lattice), the resolvent (resp. the Césàro means) of a mean-bounded semi-group of operators (resp. of positive operators) is (resp. are) strongly convergent. The mean ergodic theorem fails for mean-bounded operators which are not necessarily positive

Size of random Galois lattices and number of frequent itemsets

19 pagesWe compute the mean and the variance of the size of the Galois lattice built from a random matrix with i.i.d. Bernoulli(p) entries. Then, obseving that closed frequent itemsets are in bijection with winning coalitions, we compute the mean and the variance of the number of closed frequent itemsets. This can be of interest for mining association rules

Physical Quality of Ela Sago Biscuits Fermented by Local Microorganism (MOL) with Molasses after Storage

The purpose of this study was to determine the physical quality of ela sago biscuits fermented by MOL with molasses after being stored. This research was conducted at the Feed Engineering Technology Laboratory, Department of Animal Husbandry Faculty of Agriculture Pattimura University Ambon, which took place from March to May 2023. The material used for this research was fermented MOL sago elas biscuits with molasses which were stored for 2 months. The equipment used is digital scales, mixing bowls, grinders, oven, mixing spoons, biscuit presses, trays, plastic bags, water, aluminum filters, label paper and stationery. The variables observed were the physical quality of the biscuits including color, aroma, texture, weight, and water absorption. Research is an experiment, and the observed data were analyzed descriptively. The results showed that fermented MOL ela sago biscuits with Molasses after 2 months of storage there was a change in physical quality. The physical quality of fermented MOL ela sago biscuits with molasses underwent changes in physical quality in terms of weight, color, aroma, and water absorption

Book review: Disability studies: Emerging Insights and Perspectives

Book review: Disability studies: Emerging Insights and Perspectives Edited by: Thomas Campbell, Fernando Fontes, Laura Hemingway, Armineh Soorenian and Chris TillThe Disability Press, Leeds. 2008. 

The human homologue of unc-93 maps to chromosome 6q27 – characterisation and analysis in sporadic epithelial ovarian cancer

BACKGROUND: In sporadic ovarian cancer, we have previously reported allele loss at D6S193 (62%) on chromosome 6q27, which suggested the presence of a putative tumour suppressor gene. Based on our data and that from another group, the minimal region of allele loss was between D6S264 and D6S149 (7.4 cM). To identify the putative tumour suppressor gene, we established a physical map initially with YACs and subsequently with PACs/BACs from D6S264 to D6S149. To accelerate the identification of genes, we sequenced the entire contig of approximately 1.1 Mb. Seven genes were identified within the region of allele loss between D6S264 and D6S149. RESULTS: The human homologue of unc-93 (UNC93A) in C. elegans was identified to be within the interval of allele loss centromeric to D6S149. This gene is 24.5 kb and comprises of 8 exons. There are two transcripts with the shorter one due to splicing out of exon 4. It is expressed in testis, small intestine, spleen, prostate, and ovary. In a panel of 8 ovarian cancer cell lines, UNC93A expression was detected by RT-PCR which identified the two transcripts in 2/8 cell lines. The entire coding sequence was examined for mutations in a panel of ovarian tumours and ovarian cancer cell lines. Mutations were identified in exons 1, 3, 4, 5, 6 and 8. Only 3 mutations were identified specifically in the tumour. These included a c.452G>A (W151X) mutation in exon 3, c.676C>T (R226X) in exon 5 and c.1225G>A(V409I) mutation in exon 8. However, the mutations in exon 3 and 5 were also present in 6% and 2% of the normal population respectively. The UNC93A cDNA was shown to express at the cell membrane and encodes for a protein of 60 kDa. CONCLUSIONS: These results suggest that no evidence for UNC93A as a tumour suppressor gene in sporadic ovarian cancer has been identified and further research is required to evaluate its normal function and role in the pathogenesis of ovarian cancer

Mean ergodicity and spectrum of the Cesàro operator on weighted c0 spaces

[EN] A detailed investigation is made of the continuity, the compactness and the spectrum of the Cesàro operator C acting on the weighted Banach sequence space c0(w) for a bounded, strictly positive weight w. New features arise in the weighted setting (e.g. existence of eigenvalues, compactness, mean ergodicity) which are not present in the classical setting of c0.The research of the first two authors was partially supported by the Projects MTM2013-43540-P, GVA Prometeo II/2013/013 and ACOMP/2015/186 (Spain).Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2016). Mean ergodicity and spectrum of the Cesàro operator on weighted c0 spaces. Positivity. 20:761-803. https://doi.org/10.1007/s11117-015-0385-xS76180320Akhmedov, A.M., Başar, F.: On the fine spectrum of the Cesàro operator in $$c_0$$ c 0 . Math. J. Ibaraki Univ. 36, 25–32 (2004)Akhmedov, A.M., Başar, F.: The fine spectrum of the Cesàro operator $$C_1$$ C 1 over the sequence space $$bv_p, (1 \le p < \infty )$$ b v p , ( 1 ≤ p < ∞ ) . Math. J. Okayama Univ. 50, 135–147 (2008)Albanese, A.A., Bonet, J., Ricker, W.J.: Convergence of arithmetic means of operators in Fréchet spaces. J. Math. Anal. Appl. 401, 160–173 (2013)Albanese, A.A., Bonet, J., Ricker, W.J.: Spectrum and compactness of the Cesàro operator on weighted $$\ell _p$$ ℓ p spaces. J. Aust. Math. Soc. 99, 287–314 (2015)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in the Fréchet spaces $$\ell ^{p+}$$ ℓ p + and $$L ^{p-}$$ L p - . Glasg. Math. J (to appear)Ansari, S.I., Bourdon, P.S.: Some properties of cyclic operators. Acta Sci. Math. Szeged 63, 195–207 (1997)Brown, A., Halmos, P.R., Shields, A.L.: Cesàro operators. Acta Sci. Math. Szeged 26, 125–137 (1965)Curbera, G.P., Ricker, W.J.: Spectrum of the Cesàro operator in $$\ell ^p$$ ℓ p . Arch. Math. 100, 267–271 (2013)Curbera, G.P., Ricker, W.J.: Solid extensions of the Cesàro operator on $$\ell ^p$$ ℓ p and $$c_0$$ c 0 . Integr. Equ. Oper. Theory 80, 61–77 (2014)Curbera, G.P., Ricker, W.J.: The Cesàro operator and unconditional Taylor series in Hardy spaces. Integr. Equ. Oper. Theory 83, 179–195 (2015)Diestel, J.: Sequences and Series in Banach Spaces. Springer, New York (1984)Dowson, H.R.: Spectral Theory of Linear Operators. Academic Press, London (1978)Dunford, N., Schwartz, J.T.: Linear Operators I: General Theory, 2nd Printing. Wiley Interscience Publ, New York (1964)Emilion, R.: Mean-bounded operators and mean ergodic theorems. J. Funct. Anal. 61, 1–14 (1985)Goldberg, S.: Unbounded Linear Operators: Theory and Applications. Dover Publ, New York (1985)Hille, E.: Remarks on ergodic theorems. Trans. Am. Math. Soc. 57, 246–269 (1945)Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)Krengel, U.: Ergodic Theorems. de Gruyter, Berlin (1985)Leibowitz, G.: Spectra of discrete Cesàro operators. Tamkang J. Math. 3, 123–132 (1972)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)Megginson, R.E.: An Introduction to Banach Space Theory. Springer, New York (1998)Mureşan, M.: A Concrete Approach to Classical Analysis. Springer, Berlin (2008)Okutoyi, J.I.: On the spectrum of $$C_1$$ C 1 as an operator on $$bv_0$$ b v 0 . J. Aust. Math. Soc. Ser. A 48, 79–86 (1990)Radjavi, H., Tam, P.-W., Tan, K.-K.: Mean ergodicity for compact operators. Studia Math. 158, 207–217 (2003)Reade, J.B.: On the spectrum of the Cesàro operator. Bull. Lond. Math. Soc. 17, 263–267 (1985)Rhoades, B.E., Yildirim, M.: The spectra and fine spectra of factorable matrices on $$c_0$$ c 0 . Math. Commun. 16, 265–270 (2011)Taylor, A.E.: Introduction to Functional Analysis. Wiley, New York (1958