Note on s0s_0 nonmeasurable unions

In this note we consider an arbitrary families of sets of $s_0$ ideal introduced by Marczewski-Szpilrajn. We show that in any uncountable Polish space $X$ and under some combinatorial and set theoretical assumptions (cov(s_0)=\c for example), that for any family \ca\subseteq s_0 with \bigcup\ca =X, we can find a some subfamily \ca'\subseteq\ca such that the union \bigcup\ca' is not $s$-measurable. We have shown a consistency of the cov(s_0)=\omega_1<\c and existence a partition of the size $\omega_1$ \ca\in [s_0]^{\omega} of the real line \bbr, such that there exists a subfamily \ca'\subseteq\ca for which \bigcup\ca' is $s$-nonmeasurable. We also showed that it is relatively consistent with ZFC theory that \omega_1<\c and existence of m.a.d. family \ca such that \bigcup\ca is $s$-nonmeasurable in Cantor space $2^\omega$ or Baire space $\omega^\omega$. The consistency of $a<cov(s_0)$ and $cov(s_0)<a$ is proved also.Comment: 12 page

Taking the Stage by Storm: Theatre of, by, and for the youth in Kolkata, India

Recent high school graduates and college-goers are spearheading a youth theatre movement in Kolkata, creating a thriving parallel to the mainstream Bengali group theatre in the city. [1] Although dismissed by the theatre fraternity as a mere youthful adventure, the youth theatre is very much present and is, in many ways, paving the way for the future of Bengali language theatre. In this paper, I will study the work of three youth theatre groups focusing on organization, funding, and working process. At the end of the essay I will be reviewing six productions by these youth theatre groups from Kolkata: God\u27s Toilet and Amra Bangali Jati (We the Bengalis) by Hypokrites, A Good Play and The Burqa, The Bikini and Other Veils by M.A.D. (Mad About Drama) and Biswasta Jalojan o Aloukik Arohira (The Trusted Ship and Remarkable Passengers) and Nobel Chor (Nobel Prize thief) by 4th Bell Theatres. I selected these three groups for their consistency in producing new work and because of the leading role that they have taken in giving this theatre movement its shape and form

Dense heteroclinic tangencies near a Bykov cycle

This article presents a mechanism for the coexistence of hyperbolic and non-hyperbolic dynamics arising in a neighbourhood of a Bykov cycle where trajectories turn in opposite directions near the two nodes --- we say that the nodes have different chirality. We show that in the set of vector fields defined on a three-dimensional manifold, there is a class where tangencies of the invariant manifolds of two hyperbolic saddle-foci occur densely. The class is defined by the presence of the Bykov cycle, and by a condition on the parameters that determine the linear part of the vector field at the equilibria. This has important consequences: the global dynamics is persistently dominated by heteroclinic tangencies and by Newhouse phenomena, coexisting with hyperbolic dynamics arising from transversality. The coexistence gives rise to linked suspensions of Cantor sets, with hyperbolic and non-hyperbolic dynamics, in contrast with the case where the nodes have the same chirality. We illustrate our theory with an explicit example where tangencies arise in the unfolding of a symmetric vector field on the three-dimensional sphere

Recessive lethal mutations in Anopheles albimanus.

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Global bifurcations close to symmetry

Heteroclinic cycles involving two saddle-foci, where the saddle-foci share both invariant manifolds, occur persistently in some symmetric differential equations on the 3-dimensional sphere. We analyse the dynamics around this type of cycle in the case when trajectories near the two equilibria turn in the same direction around a 1-dimensional connection - the saddle-foci have the same chirality. When part of the symmetry is broken, the 2-dimensional invariant manifolds intersect transversely creating a heteroclinic network of Bykov cycles. We show that the proximity of symmetry creates heteroclinic tangencies that coexist with hyperbolic dynamics. There are n-pulse heteroclinic tangencies - trajectories that follow the original cycle n times around before they arrive at the other node. Each n-pulse heteroclinic tangency is accumulated by a sequence of (n+1)-pulse ones. This coexists with the suspension of horseshoes defined on an infinite set of disjoint strips, where the first return map is hyperbolic. We also show how, as the system approaches full symmetry, the suspended horseshoes are destroyed, creating regions with infinitely many attracting periodic solutions

Workplace stress in Portuguese oncology nurses delivering palliative care: A pilot study

Oncology nurses often face complex end-of-life issues, underlining their need for specific training in palliative care. In this context, nurses experience several emotional and psychological dilemmas, which are often difficult to manage and result in high levels of workplace stress. This study aimed to determine the levels and work-related factors of workplace stress among oncology nurses. A descriptive baseline study was performed as part of a large four-phase study based on quantitative data collected from Portuguese oncology nurses. Of the 32 participating nurses, most were women, and the mean age was 42.69 10.04 years. Overall, nurses revealed moderate levels of stress. Younger nurses with less professional experience had difficulties dealing with issues related to death and dying. This pilot study supported the development of a program of six Stress Management Training Workshops (SMTW) to reduce stress and increase adaptative strategies. Assessing workplace stress among oncology nurses should be the focus of intervention by managers and institutional leaders.info:eu-repo/semantics/publishedVersio

Saccharinity

We present a method to iterate finitely splitting lim-sup tree forcings along non-wellfounded linear orders. We apply this method to construct a forcing (without using an inaccessible or amalgamation) that makes all definable sets of reals measurable with respect to a certain (non-ccc) ideal