Abstract For a connected real Lie group G we consider the canonical standard-ordered star product arising from global symbol calculus based on half-commutator connection of . This trivially converges polynomial functions $$T^*G$$ T ∗ G </mml:...

We study a presentation of the Khovanov - Lauda Rouquier's candidate 2-categorification quantum group using algebraic rewriting methods. use computational approach based on modulo isotopy axioms its pivotal structure to compute family linear bases for all vector spaces 2-cells this 2-category. show that these correspond and Lauda's conjectured generating sets, proving non-degeneracy their diagr...

We prove that a family of polynomials encoding a Graph Ordering Principle (GOP(G)) requires refutations in Polynomial Calculus (PC) and Polynomial Calculus with Resolution (PCR) of degree Ω(n). Here n is the number of vertices in the graph G. This is the first linear degree lower bound for PC and PCR refutations for ordering principles. Our result answers to a question raised by Bonet and Gales...

We set out to demonstrate that the Rényi entropies with parameter α are better thought of as operating in a type of non-linear semiring called a positive semifield. We show how the Rényi’s postulates lead to Pap’s g-calculus where the functions carrying out the domain transformation are Renyi’s information function and its inverse. In its turn, Pap’s g-calculus under Rényi’s information functio...

Let G be an exceptional Lie group with T ⊂ G a maximal torus. We express the integral cohomology ring H(G/T ) by a minimal set of Schubert classes on G/T . This completes the program of determining the integral cohomology of all complete flag manifolds G/T in the context of Schubert calculus. The results are used in [DZ3] to construct the integral cohomology of a simple Lie group G in terms of ...

A rare case of giant vesical calculus weighing 1,365 g and presenting as vesicocutaneous fistula is described. Dr. Hanif G. Motiwala, ‘AMAN’ Opp.: Parasbaug Society, Behind Tagore Hall, Ellisbridge, Ahmedabad-380 006 (India) Introduction The incidence of vesical calculi is decreasing in the West, but the situation is not much altered in developing countries. The size of vesical calculi varies, ...

All standard ‘linear’ boolean equations are shown to be computationally realized within a suitable classical sequent calculus LKp. Specifically, LKp can be equipped with a cut-elimination compatible equivalence on derivations based upon reversibility properties of logical rules. So that any pair of derivations, without structural rules, of F ⇒ G and G ⇒ F , where F , G are first-order formulas ...

We classify all 4-dimensional first order bicovariant calculi on the Jordanian quantum group GLh,g(2) and all 3-dimensional first order bicovariant calculi on the Jordanian quantum group SLh(2). In both cases we assume that the bicovariant bimodules are generated as left modules by the differentials of the quantum group generators. It is found that there are 3 1-parameter families of 4-dimensio...

We prove a chain rule in the Goodwillie calculus of functors from spectra to spectra. We show that the derivatives of a composite FG at a base object X are given by taking the composition product of the derivatives of F at G(X) with the derivatives of G at X . Our proof also allows us to say something about the Taylor tower of FG (and not just its layers) in terms of the Taylor towers of F and G.

We study the low-energy effective theory of N = 2 supersymmetric Yang-Mills theory with the exceptional gauge group G 2. We obtain the Picard-Fuchs equations for the G 2 spectral curve and compute multi-instanton contribution to the prepotential. We find that the spectral curve is consistent with the microscopic su-persymmetric instanton calculus. It is also shown that G 2 hyperelliptic curve d...