λx.S ◦A instead of λx.(A[S]) S ◦ λx.A instead of (λx.A)[S] λx.S2 ◦ S1 ◦ A instead of λx.(A[S1][S2]) S2 ◦ λx.S1 ◦ A instead of (λx.A[S1])[S2] S2 ◦ S1 ◦ λx.A instead of (λx.A)[S1][S2] And so on. Far fewer parentheses. And very close to notation of category theory. If we have composition of substitutions (not in my calculus), then λx.(S2 ◦ S1) ◦ A means λx.(A[S1 ◦ S2]) From the point of view of ca...

Syntax L3.3 k nat num(k) expr t1 expr t2 expr plus(t1, t2) expr t1 expr t2 expr times(t1, t2) expr Now we specify the proper relation between concrete and abstract syntax through several simultaneously inductive judgments. Perhaps the easiest way to generate these judgments is to add the corresponding abstract syntax terms to each of the inference rules defining the concrete syntax. 0 D←→ 0 nat...

We provide an example of two closed sets S1, S2 ⊂ IR such that S1∩S2 = {0}. Yet, at the origin, a Boltyanskii tangent cone C1 to S1 and the Clarke tangent cone C2 to S2 are strongly transversal. This settles a question originally proposed by H. Sussmann. 1 Introduction Let t 7→ x∗(t) and t 7→ u∗(t) be respectively a trajectory and an optimal control for the Mayer problem    minimize φ ( x(...

to evaluate the relationship between total organic carbon (toc) and rock-eval s2 (petroleum potential) of petroleum source rocks, atotal of 180 outcrop samples from the black organic matter–rich facies of mesozoic strata from a locality of southwest of iran wereinvestigated using rock-eval vi pyrolysis and leco carbon analyzer. the linear regression is applied to determine the correlationbetwee...

Three groups of gestating gilts and sows (Exp. 1; n = 98) were used to determine the effects of Pichia guilliermondii (Pg), a whole yeast product (CitriStim, ADM Alliance Nutrition), on dam and litter immune parameters. At breeding, gilts and sows were allotted to 1 of 3 treatments maintained through lactation: sow control (SC) diet or SC supplemented with 0.1 (S1) or 0.2% (S2) Pg. Pigs from gr...

this study was carried out to investigate the direct and indirect responses to selection for four-week body weight (4 week body (wk bw)) and four-week breast weight (4 week breast weight (wk brw)) and to determine the genetic contribution of reminder founders to the last generation. a total number of 351 birds were equally allocated to three lines, including two selected lines (s1 and s2 for bw...

We investigate the asymptotic behavior of the entropy numbers of the compact embedding B1 p1,q1(R d , α) ↪→ B2 p2,q2(R ). Here Bs p,q (R d , α) denotes a weighted Besov space, where the weight is given by wα(x) = (1 + |x |2)α/2, and B2 p2,q2 (Rd ) denotes the unweighted Besov space, respectively. We shall concentrate on the so-called limiting situation given by the following constellation of pa...

The starfish SALMFamide neuropeptides S1 (GFNSALMFamide) and S2 (SGPYSFNSGLTFamide) are the prototypical members of a family of neuropeptides that act as muscle relaxants in echinoderms. Comparison of the bioactivity of S1 and S2 as muscle relaxants has revealed that S2 is ten times more potent than S1. Here we investigated a structural basis for this difference in potency by comparing the bioa...

A previous paper (West 2005) tackled the issue of calculating accurate uni-, biand trivariate normal probabilities. This has important applications in the pricing of multi-asset options, e.g. rainbow options. In this paper, we derive the Black–Scholes prices of several styles of (multi-asset) rainbow options using change-of-numeraire machinery. Hedging issues and deviations from the Black-Schol...

To evaluate the relationship between total organic carbon (TOC) and Rock-Eval S2 (petroleum potential) of petroleum source rocks, atotal of 180 outcrop samples from the black organic matter–rich facies of Mesozoic strata from a locality of southwest of Iran wereinvestigated using Rock-Eval VI pyrolysis and Leco Carbon Analyzer. The linear regression is applied to determine the correlationbetwee...