Up Close: Reinvention 101

What happens when the smart plan gives way to the ideal plan

Densities for sets of natural numbers vanishing on a given family

Abstract upper densities are monotone and subadditive functions from the power set of positive integers into the unit real interval that generalize the upper densities used in number theory, including the upper asymptotic density, the upper Banach density, and the upper logarithmic density. At the open problem session of the Workshop ``Densities and their application'', held at St. \'{E}tienne in July 2013, G. Grekos asked a question whether there is a ``nice'' abstract upper density, whose the family of null sets is precisely a given ideal of subsets of $\mathbb{N}$, where ``nice'' would mean the properties of the familiar densities consider in number theory. In 2018, M. Di Nasso and R. Jin (Acta Arith. 185 (2018), no. 4) showed that the answer is positive for the summable ideals (for instance, the family of finite sets and the family of sequences whose series of reciprocals converge) when ``nice'' density means translation invariant and rich density (i.e. density which is onto the unit interval). In this paper we extend their result to all ideals with the Baire property

A possible solution to decrease excessive single use bag waste.

Award for Best Our Husky Compact Reflection: Act with Personal Integrity and Civic Responsibility . Abstract My project requires people to reflect on their plastic/paper bag usage and how that affects their surroundings. Additionally, this may lead to a person becoming more self-aware on their waste production and help them to think of responsible ways to decrease wastefulness, creating a sense of empowerment. Requiring people to pay for each plastic or paper bag they use is one incentive to decrease or cease their usage. People will have to reason with themselves if it is worth paying the fee or if they want to avoid it. Some may become creative, finding ways to reuse their plastic or paper bags, in order to justify the fee. Some may start using reusable bags as one way to get around paying the fee. This project is research and survey based

Photocatalytic Activity of TiO

TiO2-WO3 photocatalysts were prepared in a vacuum evaporator by impregnation of TiO2 with WO2 dissolved in an H2O2 solution (30%) and followed by calcination at 400 and 600∘C. XRD analyses showed that at 400∘C monoclinic phase of WO3 was dominated whereas at 600∘C both monoclinic and regular phases of WO3 were present. Modification of TiO2 by WO3 caused increasing in the absorption of light to the visible range. TiO2 and photocatalysts modified with low amount of WO3 (1–5 wt.%) showed high adsorption of Acid Red (AR) on their surface and enhanced photocatalytic activity under UV irradiation. Under visible light irradiation, TiO2-WO3 photocatalysts prepared at 400∘C were more active for AR decomposition than those prepared at 600∘C suggesting that monoclinic phase of WO3 is more active under visible light than regular WO3. Although TiO2-WO3 photocatalysts appeared to be active under visible light for decomposition of AR, the UV irradiation was more efficient

On the structure of Borel ideals in-between the ideals \ED and \fin\otimes\fin in the Kat\v{e}tov order

For a family \cF\subseteq \omega^\omega we define the ideal \I(\cF) on $\omega\times\omega$ to be the ideal generated by the family \{A\subseteq \omega\times\omega:\exists f\in \cF\,\forall^\infty n\, (|\{k:(n,k)\in A\}|\leq f(n))\}. Using ideals of the form \I(\cF), we show that the structure of Borel ideals in-between two well known Borel ideals \ED = \{A\subseteq\omega\times\omega:\exists m \, \forall^\infty n\, (|\{k:(n,k)\in A\}| and \fin\otimes\fin = \{A\subseteq\omega\times\omega:\forall^\infty n \, (|\{k:(n,k)\in A\}|<\aleph_0))\} in the Kat\v{e}tov order is fairly complicated. Namely, there is a copy of \cP(\omega)/\fin in-between \ED and \fin\otimes\fin, and consequently there are increasing and decreasing chains of length \bnumber and antichains of size \continuum

Reversible temperature regulation of electrical and thermal conductivity using liquid–solid phase transitions

Reversible temperature tuning of electrical and thermal conductivities of materials is of interest for many applications, including seasonal regulation of building temperature, thermal storage and sensors. Here we introduce a general strategy to achieve large contrasts in electrical and thermal conductivities using first-order phase transitions in percolated composite materials. Internal stress generated during a phase transition modulates the electrical and thermal contact resistances, leading to large contrasts in the electrical and thermal conductivities at the phase transition temperature. With graphite/hexadecane suspensions, the electrical conductivity changes 2 orders of magnitude and the thermal conductivity varies up to 3.2 times near 18 °C. The generality of the approach is also demonstrated in other materials such as graphite/water and carbon nanotube/hexadecane suspensions

How shared pre-start-up moments of transition and cognitions contextualize effectual and causal decisions in entrepreneurial teams

Although it is reported that early venture decisions are influenced by the relationships and common history of entrepreneurial team members, little is known about how the mutual interests and ambitions experienced in the pre-start-up phase provide a shared and relational context for joint decisions. Drawing on a multiple case study approach of nine entrepreneurial teams in new ventures, this study identifies the shared pre-start-up moments of transition during which team members’ prior work and life patterns start to change. We show that in these intense moments, shared entrepreneurial cognition evolves among team members – the relationality of which provides a unique social context for decision behaviors. Our findings conclude that effectual behaviors advance a theory of context because in simultaneously working with effectual and causal logics (albeit with varying intensities), team decisions are realized that are consistent with the relational context that emerges in the pre-start-up moment