Hydrodynamic correlation functions of a driven granular fluid in steady state

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. Inelastic collisions are modeled by incomplete normal restitution, allowing for efficient simulations with an event-driven algorithm. The incoherent scattering function Fincoh(q,t ) is seen to follow time-density superposition with a relaxation time that increases significantly as the volume fraction increases. The statistics of particle displacements is approximately Gaussian. For the coherent scattering function S(q,ω), we compare our results to the predictions of generalized fluctuating hydrodynamics, which takes into account that temperature fluctuations decay either diffusively or with a finite relaxation rate, depending on wave number and inelasticity. For sufficiently small wave number q we observe sound waves in the coherent scattering function S(q,ω) and the longitudinal current correlation function Cl(q,ω). We determine the speed of sound and the transport coefficients and compare them to the results of kinetic theory.

Prime and Semiprime Inner Functions

This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided.

Prime and semiprime inner functions

Abstract This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided.

Equality of P-partition Generating Functions

To every partially ordered set (poset), one can associate a generating function, known as the P-partition generating function. We find necessary conditions and sufficient conditions for two posets to have the same P-partition generating function. We define the notion of a jump sequence for a labeled poset and show that having equal jumpsequences is a necessary condition for generating function equality. We also develop multiple ways of modifying posets that preserve generating function equality. Finally, we are able to give a complete classification of equalities among partially ordered setswith exactly two linear extensions.

Comparing skew Schur functions: a quasisymmetric perspective

Reiner, Shaw and van Willigenburg showed that if two skew Schur functions sA and sB are equal, then the skew shapes $A$ and $B$ must have the same "row overlap partitions." Here we show that these row overlap equalities are also implied by a much weaker condition than Schur equality: that sA and sB have the same support when expanded in the fundamental quasisymmetric basis F. Surprisingly, there is significant evidence supporting a conjecture that the converse is also true. In fact, we work in terms of inequalities, showing that if the F-support of sA contains that of sB, then the row overlap partitions of A are dominated by those of B, and again conjecture that the converse also holds. Our evidence in favor of these conjectures includes their consistency with a complete determination of all F-support containment relations for F-multiplicity-free skew Schur functions. We conclude with a consideration of how some other quasisymmetric bases fit into our framework.

The Effects of Hibernation on Immunological Functions in Female Big Brown Bats (Eptesicus fuscus)

The emerging disease White-Nose Syndrome in hibernating bat populations across the United States has increased the need to understand the physiological benefits and consequences of hibernation and the effects on immunological responsiveness. Hibernation has been well-documented in many mammalian species, yet few studies have examined hibernation immunology in bats, particularly with respect to normal immunological patterns. In order to characterize the levels of circulating leukocytes and plasma immunoglobulins in euthermic and hibernating female big brown bats (Eptesicus fuscus), blood smear differential leukocyte counts and total immunoglobulin assays were performed for each group using blood samples from the active and hibernation seasons. Hibernation patterns – torpor and arousals from torpor – were determined by placing temperature-sensitive dataloggers on the backs of bats assigned to the hibernating group during the hibernation season. Data indicate that the ratio of circulating neutrophils to lymphocytes is lower in bats assigned to the euthermic group during the hibernation season than in bats assigned to the hibernation group during the hibernation period, but that relative immunoglobulin levels do not differ during the hibernation season, regardless of whether bats were active or hibernating. Neither bats assigned to the hibernation group nor bats assigned to the euthermic group demonstrate a significant change in the ratio of circulating neutrophils and lymphocytes between their active and hibernating seasons. Bats assigned to the hibernation group were also observed to arouse from torpor somewhat synchronously. These results suggest that innate and adaptive cell levels are maintained, at best, in hibernating bats that are not immunologically challenged and that bats that remain euthermic during the hibernation season are able to continually regulate their levels of neutrophils and lymphocytes and therefore their innate and adaptive immune system responses.