Diagonals of rational functions, pullbacked 2F1 hypergeometric functions and modular forms (unabrigded version)

We recall that diagonals of rational functions naturally occur in lattice statistical mechanics and enumerative combinatorics. We find that a seven-parameter rational function of three variables with a numerator equal to one (reciprocal of a polynomial of degree two at most) can be expressed as a pullbacked 2F1 hypergeometric function. This result can be seen as the simplest non-trivial family of diagonals of rational functions. We focus on some subcases such that the diagonals of the corresponding rational functions can be written as a pullbacked 2F1 hypergeometric function with two possible rational functions pullbacks algebraically related by modular equations, thus showing explicitely that the diagonal is a modular form. We then generalise this result to eight, nine and ten parameters families adding some selected cubic terms at the denominator of the rational function defining the diagonal. We finally show that each of these previous rational functions yields an infinite number of rational functions whose diagonals are also pullbacked 2F1 hypergeometric functions and modular forms.Comment: 39 page

The Elasticity of Demand for Gasoline in China

This paper estimates the price and income elasticities of demand for gasoline in China. Our estimates of the intermediate-run price elasticity of gasoline demand range between -0.497 and -0.196, and our estimates of the intermediate-run income elasticity of gasoline demand range between 1.01 and 1.05. We also extend previous studies to estimate the vehicle miles traveled (VMT) elasticity and obtain a range from -0.882 to -0.579

Intra-articular injection of the cyclooxygenase-2 inhibitor parecoxib attenuates osteoarthritis progression in anterior cruciate ligament-transected knee in rats: role of excitatory amino acids

SummaryObjectiveOur present study examined the effect of intra-articular cyclooxygenase-2 (COX-2) inhibitor parecoxib on osteoarthritis (OA) progression and the concomitant changes in excitatory amino acids' (EAAs) levels of the anterior cruciate ligament-transected (ACLT) knee joint dialysates.MethodsOA was induced in Wistar rats by anterior cruciate ligament transection of the knee of one hindlimb, the other was left unoperated and untreated. Rats were placed into four groups: Group ACLT/P received intra-articular parecoxib injection (100μg) in the ACLT knee once a week for 5 consecutive weeks starting at 8 weeks after surgery. Group ACLT/S received the same procedure as group ACLT/P with saline injection instead. Naïve (Naïve/P) rats received only intra-articular parecoxib injection in one knee once a week for 5 consecutive weeks without surgery. The sham-operated rats underwent arthrotomy only without treatment. Twenty weeks after surgery, knee joint dialysates were collected and EAAs' concentration was assayed by high-performance liquid chromatography, and gross morphology and histopathology (Mankin and synovitis grading) were examined on the medial femoral condyles and synovia.ResultsParecoxib alone had no effect on cartilage and synovium of normal knees in Naïve/P rats. In ACLT/P rats, parecoxib treatment showed a significant inhibition of cartilage degeneration of the medial femoral condyle at both the macroscopic level (1.15±0.17 vs 2.55±0.12, P<0.05) and the Mankin scores (3.03±0.28 vs 8.82±0.43, P<0.05). Intra-articular parecoxib injection also suppressed the synovial inflammation of ACLT joint compared to the ACLT/S group (3.92±0.41 vs 9.25±0.32, P<0.05). Moreover, glutamate and aspartate levels were also significantly reduced in the ACLT/P group compared to the ACLT/S group by parecoxib treatment (91.2±9.4% vs 189.5±17.0%, P<0.05 and 98.2±11.6% vs 175.3±12.4%, P<0.05, respectively).ConclusionThis study shows that intra-articular injection of COX-2 inhibitor parecoxib inhibits the ACLT-induced OA progression; it was accompanied by a reduction of glutamate and aspartate concentration in the ACLT joint dialysates. From our present results, we suggested that intra-articular parecoxib injection, in addition to the anti-inflammatory effect, inhibiting the EAAs' release, may also play a role in inhibiting the traumatic knee injury induced OA progression

Vector theories in cosmology

This article provides a general study of the Hamiltonian stability and the hyperbolicity of vector field models involving both a general function of the Faraday tensor and its dual, $f(F^2,F\tilde F)$, as well as a Proca potential for the vector field, $V(A^2)$. In particular it is demonstrated that theories involving only $f(F^2)$ do not satisfy the hyperbolicity conditions. It is then shown that in this class of models, the cosmological dynamics always dilutes the vector field. In the case of a nonminimal coupling to gravity, it is established that theories involving $R f(A^2)$ or $Rf(F^2)$ are generically pathologic. To finish, we exhibit a model where the vector field is not diluted during the cosmological evolution, because of a nonminimal vector field-curvature coupling which maintains second-order field equations. The relevance of such models for cosmology is discussed.Comment: 17 pages, no figur