Vanishing and Non-Vanishing Criteria for Branching Schubert Calculus by Kevin Purbhoo Doctor of Philosophy in Mathematics University of California at Berkeley Professor Allen Knutson, Chair We investigate several related vanishing problems in Schubert calculus. First we consider the multiplication problem. For any complex reductive Lie group G, many of the structure constants of the ordinary co...

We develop a notion of nonlinear expectation —-G–expectation—generated by a nonlinear heat equation with infinitesimal generator G. We first study multi-dimensional G–normal distributions. With this nonlinear distribution we can introduce our G–expectation under which the canonical process is a multi–dimensional G–Brownian motion. We then establish the related stochastic calculus, especially st...

We introduce a notion of nonlinear expectation —-G–expectation—generated by a nonlinear heat equation with a given infinitesimal generator G. We first discuss the notion of G–standard normal distribution. With this nonlinear distribution we can introduce our G–expectation under which the canonical process is a G–Brownian motion. We then establish the related stochastic calculus, especially stoc...

This paper presents rules in sequent calculus for a binary quantifier $I$ to formalise definite descriptions: $Ix[F, G]$ means `The $F$ is $G$'. The are suitable be added system of positive free logic. extends the proof cut elimination theorem this by Indrzejczak proving cases $I$. There also brief comparisons present approach more common one that formalises descriptions with term forming opera...

Several approaches to the formulation of a fractional theory calculus "variable order" have appeared in literature over years. Unfortunately, most these proposals lack rigorous mathematical framework. We consider an alternative view on problem, originally proposed by G. Scarpi early seventies, based naive modification representation Laplace domain standard kernels functions involved (constant-o...

We develop the generalized Cartan Calculus for the groups G = SL(2,R) × R +, SL(5,R) and SO(5, 5). They are the underlying algebraic structures of d = 9, 7, 6 exceptional field theory, respectively. These algebraic identities are needed for the “tensor hierarchy” structure in exceptional field theory. The validity of Poincaré lemmas in this new differential geometry is also discussed. Finally w...

introduction here we report an unusual case of massive stone formation in augmented urinary bladder. case presentation a 25-year-old man presented with recurrent urinary tract infection ten years after augmentation cystoplasty after a complex pelvic fracture urethral distraction defect. on evaluation by ultrasonography, x-ray, and computed tomography of abdomen showed large burden of stones in ...

The multiindex Mittag-Leffler (M-L) function and the multiindex Dzrbashjan-Gelfond-Leontiev (D-G-L) differentiation and integration play a very pivotal role in the theory and applications of generalized fractional calculus. The object of this paper is to investigate the relations that exist between the Riemann-Liouville fractional calculus and multiindex Dzrbashjan-Gelfond-Leontiev differentiat...

introdouction: overhang refers to the extension of restoration material from the cavity. it has an important role in decay, plaque accumulation and periodontal disease, so the aim of this study is determining the frequency of restoration overhang in patients in anzali, guilan. materials and methods: this descriptive cross-sectional study was completed using 293 patients who visited for routine ...

We apply the semantic tool of non-deterministic matrices to characterize two important properties of canonical Gentzen-type calculi: invertibility of rules and axiom expansion. We show that in every canonical calculus G satisfying a natural condition, the following are equivalent: (i) the connectives of G admit axiom expansion, (ii) the rules of G are invertible, and (iii) G has a characteristi...