Embeddings of non-simply-connected 4-manifolds in 7-space. II. On the smooth classification

We work in the smooth category. Let $N$ be a closed connected orientable 4-manifold with torsion free $H_1$ , where $H_q := H_q(N; {\mathbb Z} )$ . Our main result is a readily calculable classification of embeddings $N \to {\mathbb R}^7$ up to isotopy, with an indeterminacy. Such a classification was only known before for $H_1=0$ by our earlier work from 2008. Our classification is complete when $H_2=0$ or when the signature of $N$ is divisible neither by 64 nor by 9. The group of knots $S^4\to {\mathbb R}^7$ acts on the set of embeddings $N\to {\mathbb R}^7$ up to isotopy by embedded connected sum. In Part I we classified the quotient of this action. The main novelty of this paper is the description of this action for $H_1 \ne 0$ , with an indeterminacy. Besides the invariants of Part I, detecting the action of knots involves a refinement of the Kreck invariant from our work of 2008. For $N=S^1\times S^3$ we give a geometrically defined 1–1 correspondence between the set of isotopy classes of embeddings and a certain explicitly defined quotient of the set ${\mathbb Z} \oplus {\mathbb Z} \oplus {\mathbb Z} _{12}$ .

Korevaar–Schoen’s directional energy and Ambrosio’s regular Lagrangian flows

We develop Korevaar–Schoen’s theory of directional energies for metric-valued Sobolev maps in the case of $${\textsf {RCD}}$$ RCD source spaces; to do so we crucially rely on Ambrosio’s concept of Regular Lagrangian Flow. Our review of Korevaar–Schoen’s spaces brings new (even in the smooth category) insights on some aspects of the theory, in particular concerning the notion of ‘differential of a map along a vector field’ and about the parallelogram identity for $${\textsf {CAT}}(0)$$ CAT ( 0 ) targets. To achieve these, one of the ingredients we use is a new (even in the Euclidean setting) stability result for Regular Lagrangian Flows.

PENGARUH PIJAT OKSITOSIN TERHADAP KELANCARAN PENGELUARAN ASI IBU POST PARTUM PRIMIPARA DI RUANG WIDYA RUMAH SAKIT CIREMAI CIREBON TAHUN 2015

Tidak keluarnya ASI pada hari-hari pertama setelah melahirkan menjadi salah satu penyebab tidak terwujudnya pemberian ASI ekskusif. Terlambatnya pengeluaran ASI dapat disebabkan oleh terhambatnya sekresi oksitosin yang sangat berperan dalam kelancaran pengeluaran ASI. Pijat oksitosin merupakan salah satu cara yang efektif untuk merangsang sekresi oksitosin. Penelitian ini bertujuan mengetahui pengaruh pijat oksitosin terhadap pengeluaran ASI pada ibu post partum primipara di Ruang Widya Rumah Sakit Ciremai Cirebon tahun 2015.Penelitian ini merupakan jenis penelitian Quasy Experiment, populasi dalam penelitian ini adalah ibu post partum primipara di Ruang Widya Rumah Sakit Ciremai pada tanggal 11 Maret sampai 1 April 2015. Teknik pengambilan sampel yang digunakan adalah purposive sampling dengan jumlah sampel 12 responden untuk setiap kelompok. Instrumen penelitian yang digunakan adalah kuesioner dan teknik pengambilan data dengan cara penyebaran kuesioner. Penelitian menggunakan ujibeda t-test independent. Penelitian dilakukan di Ruang Widya Rumah Sakit Ciremai Cirebon pada tanggal 11 Maret sampai 1 April 2015.Dari hasil penelitian didapatkan pengeluaran ASI pada kelompok intervensi dalam kategori lancar yaitu sebanyak 75% sedangkan pada kelompok control dalam kategori tidak lancar yaitu sebanyak 75%. Hasil analisa bivariat dengan menggunakan uji beda t-test independent sample diperoleh nilai signifikansi 0,000, dibandingkan dengan nilai signifikansi α=5% (0,05) maka p value < 0,05 berarti ada pengaruh pijat oksitosin terhadap kelancaran pengeluaran ASI ibu post partum primipara.Sehubungan dengan hasil penelitian diharapkan perlunya memberikan informasi tentang pijat oksitosin ini bagi rumah sakit, ilmu keperawatan, praktik keperawatan dan ibu post partum.Kata Kunci : Pijat Oksitosin, ASI, Ibu post partum primipara, Pengeluaran ASI ABSTRACTBreast milk that doesn’t come out on first day after birthing can be one cause of not realization exclusive breastfeeding. Delayed breast milk’s output can be cause by inhibition secretion of oxytocin which very important in continuity breast milk’s output. Oxytocin massage is one of method which effective for stimulates the secretion of oxytocin. The purpose of this research is to know the effect of oxytocin massage to continuity breast milk’s output on post partumprimipara’s mother in Widya Ward Ciremai Hospital Cirebon 2015.The type of this research is Quasy Experiment, and population in this research is post partumprimipara’s mother in Widya Ward Ciremai Hospital at 11thof March until 1stof April 2015.Sample was taken by purposive sampling technique with total sample is 12 samples for each group. Instrument that used in this research is questionnaire and data collection techniques used is by distributing questionnaire. This research is using t-test independent for research statistic test. This research conducted in Widya Ward Ciremai Hospital Cirebon 11thof March until 1stof April 2015.The result of this research is most of the output breast milk in intervention group in the smooth category as much 75%, but in control group most of the output breast milk in the not smooth category as much 75%. The result of the bivariat analysis by using t-test independent is obtained p value 0,000, be compared with p value in α=5% (0,05) so p value < 0,05and there iseffect of oxytocin massage to continuity breast milk’s output on post partumprimipara’s mother in Widya Ward Ciremai Hospital Cirebon 2015.Related with the result of this researchwill needs to provide information about oxytocin massage for hospital, nursing science, nursing practice and post partum’s mother.Keyword : Oxytocyn massage, Breast milk, Post partumprimipara’s mother, breast milk’s output

Cyber Extension: Penggunaan Media dan Kelancaran Pencarian Informasi di Kalangan Penyuluh Pertanian Kabupaten Bogor

Current sustainable development of agriculture is one of which depends on the capacity of agricultural extension workers. The development of information technology contributes to the means for increasing this capacity. Cyber Extension, which is the embodiment of Law No. 16 of 2006 concerning agricultural extension systems, is expected to be fully utilized by extension agents throughout Indonesia. This is so that the instructors can provide information and develop innovations in agriculture. This study aims to explain the use of media and the stage of information seeking by instructors in Bogor district. The concept used in this research is Cyber Extension, media use and the smoothness of information retrieval. This study uses a quantitative descriptive approach with data collection techniques through surveys. A total of 61 agricultural instructors in Bogor Regency were interviewed through a closed questionnaire. In the media use variable, the results of the study show that the extension agent's ability to access is good while the availability of facilities and operational costs are still in the less category. When the smoothness of the information search process is in the smooth category.

Real-analytic AbC constructions on the torus

In this article we demonstrate a way to extend the AbC (approximation by conjugation) method invented by Anosov and Katok from the smooth category to the category of real-analytic diffeomorphisms on the torus. We present a general framework for such constructions and prove several results. In particular, we construct minimal but not uniquely ergodic diffeomorphisms and non-standard real-analytic realizations of toral translations.

How do autodiffeomorphisms act on embeddings?

We work in the smooth category. The following problem was suggested by E. Rees in 2002: describe the precomposition action of self-diffeomorphisms of Sp × Sq on the set of isotopy classes of embeddings Sp × Sq → ℝm.Let G: Sp × Sq → ℝm be an embedding such thatis null-homotopic for some pair of different points a, b ∈ Sp. We prove the following statement: if ψ is an autodiffeomorphism of Sp × Sq identical on a neighbourhood of a × Sq for some a ∈ Sp and p ⩽ q and 2m ⩾ 3p +3q + 4, then G◦ ψ is isotopic to G.Let N be an oriented (p + q)-manifold and let f, g be isotopy classes of embeddings N → ℝm, Sp × Sq → ℝm, respectively. As a corollary we obtain that under certain conditions for orientation-preserving embeddings s: Sp × Dq → N the Sp-parametric embedded connected sum f#sg depends only on f, g and the homology class of s|Sp × 0.

A Revised Version of P. L. PROPER KNOT EQUIVALENCE CLASSES ARE GENERATED BY LOCALLY FLAT ISOTOPIES (Vol. 3, No. 4 (December 94), pp. 497–509)

A p. 1. proper knot is a proper p. 1. embedding of the real line into a p. 1. open 3-manifold. Two p. 1. proper knots are said to be equivalent if there is a p. 1. proper isotopy (possibly non-ambient) connecting them. A priori such an isotopy need not be locally flat: for example a local knot in the range could be shrunk to a point within a 3-cell. In this paper we show that, in essence, this is the only type of non-locally flat phenomenon. We show that such a local knot can always be “combed to infinity”. Thus if two p. 1. proper knots are connected by a p. 1. proper isotopy then the connecting isotopy can be modified to be a locally flat p. 1. proper isotopy. Hence, in proper knot theory, the smooth category and the p. 1. category are similar.

P. L. PROPER KNOT EQUIVALENCE CLASSES ARE GENERATED BY LOCALLY FLAT ISOTOPIES

A p. 1. proper knot is a proper p. 1. embedding of the real line into a p. 1. open 3-manifold. Two p. 1. proper knots are said to be equivalent if there is a p. 1. proper isotopy (possibly non-ambient) connecting them. A priori such an isotopy need not be locally flat: for example a local knot in the range could be shrunk to a point within a 3-cell. In this paper we show that, in essence, this is the only type of non-locally flat phenomena. We show that such a local knot can always be "combed to infinity". Thus if two p. 1. proper knots are connected by a p. 1. proper isotopy then the connecting isotopy can be modified to be a locally flat p. 1. proper isotopy. Hence, in proper knot theory, the smooth category and the p. 1. category are similar.