LetX be a symplectic or odd orthogonal Grassmannian parametrizing isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove a Giambelli formula which expresses an arbitrary Schubert class in H∗(X,Z) as a polynomial in certain special Schubert classes. We introduce and study theta polynomials, a family of polynomials which are positive linear combination...

Let G be a complex semi-simple Lie group and let P, Q be a pair of parabolic subgroups of G such that Q contains P . Consider the flag varieties G/P , G/Q and Q/P . We show that certain structure constants in H∗(G/P ) with respect to the Schubert basis can be written as a product of structure constants coming from H∗(G/Q) and H∗(Q/P ) in a very natural way. The primary application is to compute...

The notion of a context in formal concept analysis and that an approximation space rough set theory are unified this study to define Kripke context. For any (G,M,I), relation on the G objects M properties included, giving structure form ((G,R), (M,S), I). A gives rise complex algebras based collections protoconcepts semiconcepts underlying On abstraction, double Boolean (dBas) with operators to...

" Mathematicians care no more for logic than logicians for mathematics. " Augustus de Morgan, 1868 Proofs are traditionally syntactic, inductively generated objects. This paper presents an abstract mathematical formulation of propositional calculus (propositional logic) in which proofs are combinatorial (graph-theoretic), rather than syntactic. It defines a combinatorial proof of a proposition ...

Modern computing paradigms for distributed applications advocate a strong control on shared resources available on demand in order to guarantee their correct usages. An illustrative example of such paradigms is Cloud Computing. In this dissertation, we study formal models for distributed applications, paying particular attention to resource usage analysis. Formal methods for specifying and anal...

the incidence of stone disease among patients with congenital renal anomalies including malrotated kidney is more than in normal population due to poor urine drainage and stasis (1). various minimally invasive options have been used for the management. ureteroscopy and holmium:yag laser lithotripsy have been reported with favorable outcomes (2). we report a 30-year-old male who presented to our...

The notion of a planar st graph (also known as e-bipolar planar graph) is essentially equivalent to that of a progressive plane graph, which was introduced by Joyal and Street in the theory of graphical calculus for tensor categories. Fraysseix and Mendez have shown a bijection between equivalence classes of planar st embeddings of a directed graph G and the conjugate orders of the edge poset o...

tonitis. The laboratory findings were haemoglobin 9.6 g/dL, haematocrit 29%, serum urea 228 mg/dL, creatinine 7.6 mg/dL, sodium 135 mEq/L, chloride 110 mEg/L, potassium 7.1 mEq/L, albumin 2.4 g/dL, arterial pH 7.29, pCO2 15.7 mmHg, HCO3 7.5 mEq/L and BE −16.0. The abdominal X-ray showed an elliptical radiopaque mass∼7 cm in its highest diameter in the bladder region (Figure 1). Daily dialysis w...

In this report, we define a sound and complete categorical semantics for the parallel λ-calculus, based on a notion of aggregation monad which is modular w.r.t. associativity, commutativity and idempotence. To prove completeness, we introduce a category of partial equivalence relations adapted to parallelism, in which any extension of the basic equational theory of the calculus is induced by so...