New species of fermions and bosons, cosmological constant problem and a farewell to spin–statistics theorem

If dark matter exists in the form of ultralight fermionic and bosonic species, then (a) it can accelerate evaporation of astrophysical black holes to the extent that their lifetimes can be reduced to astronomical time scales, a and (b) if there are extremely large number of such species it has the potential to solve the hierarchy problem [H. Davoudiasl, P. B. Denton and D. A. McGady, Phys. Rev. D 103 (2021) 055014; G. Dvali, Fortschr. Phys. 58 (2010) 528]. Here, we put forward a proposal that darkness of many of these new particles is natural, and in addition, the net zero point energy of the fermions exactly cancels that coming from the new bosons. The needed fermion–boson equality, and matching the fermion–boson degrees of freedom, comes about naturally. A very direct argument that allows the departure from the spin–statistics theorem is presented.

Incidence Category of the Young Lattice, Injections Between Finite Sets, and Koszulity

We study the quadratic quotients of the incidence category of the Young lattice defined by the zero relations corresponding to adding two boxes to the same row, or to the same column, or both. We show that the last quotient corresponds to the Koszul dual of the original incidence category, while the first two quotients are, in a natural way, Koszul duals of each other and hence they are in particular Koszul self-dual. Both of these two quotients are known to be basic representatives in the Morita equivalence class of the category of injections between finite sets. We also present a new, rather direct, argument establishing this Morita equivalence.

The L p Minkowski problem for q-capacity

In the present paper, we first introduce the concepts of the L p q-capacity measure and L p mixed q-capacity and then prove some geometric properties of L p q-capacity measure and a L p Minkowski inequality for the q-capacity for any fixed p ⩾ 1 and q > n. As an application of the L p Minkowski inequality mentioned above, we establish a Hadamard variational formula for the q-capacity under p-sum for any fixed p ⩾ 1 and q > n, which extends results of Akman et al. (Adv. Calc. Var. (in press)). With the Hadamard variational formula, variational method and L p Minkowski inequality mentioned above, we prove the existence and uniqueness of the solution for the L p Minkowski problem for the q-capacity which extends some beautiful results of Jerison (1996, Acta Math.176, 1–47), Colesanti et al. (2015, Adv. Math.285, 1511–588), Akman et al. (Mem. Amer. Math. Soc. (in press)) and Akman et al. (Adv. Calc. Var. (in press)). It is worth mentioning that our proof of Hadamard variational formula is based on L p Minkowski inequality rather than the direct argument which was adopted by Akman (Adv. Calc. Var. (in press)). Moreover, as a consequence of L p Minkowski inequality for q-capacity, we get an interesting isoperimetric inequality for q-capacity.

Integrity in Law’s Empire

In this paper I focus on Dworkin's arguments for the distinctive political virtue of integrity, arguing that we have serious reasons to doubt that the case for integrity has been made. I approach Dworkin’s complex argument in two main steps, following his two main arguments for the distinct value of integrity. The first, and more direct argument, is based on what Dworkin takes to be the grounds for rejecting “checkerboard laws”. The second argument is the one that ties the value of integrity to political legitimacy by way of articulating the value of integrity in light of its affinity with Fraternity, the idea of a “true community”, and the associative obligations such communities engender. I try to show in this paper that both of these lines of argument are not convincing.

Willingness-to-pay for Environmental Services Provided By Trees in Core and Fringe Areas of Benin City, Nigeria 1

Economic valuation of environmental services has emerged as a new and more direct argument and incentive for protection of trees and sustenance of environmental quality. This study's aim was to estimate the monetary value for conservation of urban trees and environmental services in Benin City, Nigeria. A Contingent Valuation Method involving a survey of 350 residents was adopted for the study. Flooding and erosion control, scenic beauty, provision of shade and regulation of local temperature received positive rankings and high scores. Thus, an average of US$1.20/month, which yielded an aggregate value of US$1 200 000 to US$1 860 00, was the amount Benin City residents were willing to contribute towards the conservation of trees. This study identified profession, years of residency and indigenous knowledge of ES as significant predictors that can influence willingness-to-pay. The findings provided quantitative data to demonstrate the importance of conserving trees to town planners, forest managers, policy makers and the urban community.

Introduction

In this paper I chart the evolution of my thinking on the metaphysical status of consciousness from the position defended in Purple Haze: The Puzzle of Consciousness to the present. Originally I argued that materialism is very likely true, but we still couldn’t understand how it could be true, whereas now I believe, on the basis of inference to the best explanation, that it is likely false. However, I still maintain that there is no direct argument from conceivability considerations to the falsehood of materialism. In the rest of the paper I give a brief overview of the papers included in the volume.

Trees, Trees, So Many Trees

This chapter considers the problem of counting trees. Every connected graph G has a spanning tree, that is, a connected acyclic subgraph containing all the vertices of G. If G has no cycles, it is its own unique spanning tree. If G has cycles, we can locate any cycle and delete one of its edges. Repeat this process until no cycle remains. We have just constructed one of the spanning trees of G. Typically G will have many, many spanning trees. Let us use t(G) to denote the number of spanning trees in G. There are several ways to determine t(G). Some of these are direct argument, Kirchhoff's Matrix Tree Theorem, a variation of this theorem using eigenvalues, and Prüfer codes.