directly assess these functional changes. These findings were correlated with data obtained by more classical indirect methods and further delineate the concept of a reversible alteration in membrane transport and are consistent with an in vivo swelling of skeletal muscle cells in response to severe hemorrhagic shock. Methods and MaterialsNon-splenectomized adult baboons (Papio Sp.) weighing 12-27 Kg. were anesthesized initially with a combination of intravenous Sernylan (1 mg./Kg.) and Pentobarbital (5 mg./Kg.) and maintained on small doses of Pentobarbital throughout the experiment to achieve a constant level of anesthesia. Tracheostomy was performed. Polyethylene catheters were used to cannulate the femoral artery of one leg and femoral vein of the opposite limb. Arterial pressure was constantly. mdnitored on a Sanborn recorder connected to the femobral artery cannula through a pressure transducer. Blood samples for all analyses were obtained from the femoral artery cannula and all injections were given through the femoral vein catheter.Each animal was studied throughout a standard 3-hour control period and then following induiction of hemorrhagic shock. Arterial pressures of 60 mm. Hg systolic were achieved during the first 8-10 minutes of hemorrhage and subsequent hemorrhage was carried out as needed to maintain this level of hypotension. Care was taken to avoid hemorrhage in excess of 25-30% of calculated blood volume in order to obtain a prolonged severe shock preparation. Serial determinations of skeletal muscle PD as well as blood pressure, pulse, and respiration were recorded 288Presented at the Annual Meeting of the American Surgical Association,

Given an arithmetic function a : N → R, one can associate a naturally defined, doubly infinite family of Jensen polynomials. Recent work of Griffin, Ono, Rolen, and Zagier shows that for certain families of functions a : N → R, the associated Jensen polynomials are eventually hyperbolic (i.e., eventually all of their roots are real). This work proves Chen, Jia, and Wang's conjecture that the partition Jensen polynomials are eventually hyperbolic as a special case. Here, we make this result explicit. Let N (d) be the minimal number such that for all n ≥ N (d), the partition Jensen polynomial of degree d and shift n is hyperbolic. We prove that N (3) = 94, N (4) = 206, and N (5) = 381, and in general, that N (d) ≤ (3d) 24d (50d) 3d 2 .

Dyson famously provided combinatorial explanations for Ramanujan's partition congruences modulo 5 and 7 via his rank function, and postulated that an invariant explaining all of Ramanujan's congruences modulo 5, 7, and 11 should exist. Garvan and Andrews-Garvan later discovered such an invariant called the crank, fulfilling Dyson's goal. Many further examples of congruences of partition functions are known in the literature. In this paper, we provide a framework for discovering and proving the existence of such invariants for families of congruences and partition functions. As a first example, we find a family of crank functions that simultaneously explains most known congruences for colored partition functions. The key insight is to utilize a powerful recent theory of theta blocks due to Gritsenko, Skoruppa, and Zagier. The method used here should be useful in the study of other combinatorial functions.

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In celebration of Krishnaswami Alladi's 60th birthday.Abstract If gcd(r, t) = 1, then Alladi proved the Möbius sum identityHere p min (n) is the smallest prime divisor of n. The right-hand side represents the proportion of primes in a fixed arithmetic progression modulo t. Locus generalized this to Chebotarev densities for Galois extensions. Answering a question of Alladi, we obtain analogs of these results to arithmetic densities of subsets of positive integers using q-series and integer partitions. For suitable subsets S of the positive integers with density d S , we prove thatwhere the sum is taken over integer partitions λ, µ P (λ) is a partition-theoretic Möbius function, |λ| is the size of partition λ, and sm(λ) is the smallest part of λ. In particular, we obtain partition-theoretic formulas for even powers of π when considering power-free integers.