We describe the applications of localization methods, in particular the functorial localization formula, in the proofs of several conjectures from string theory. Functorial localization formula pushes the computations on complicated moduli spaces to simple moduli spaces. It is a key technique in the proof of the general mirror formulas, the proof of the Hori-Vafa formulas for explicit expressio...

The authors discussed about the problem of special form in astigmatism classification. This special type of astigmatism is the form of obliquely crossed astigmatism. In which the meridians, major and minor, are not right angles. In this astigmatism is not possible to prescribing for cylindrical (toric) spectacle lens. Authors describe the Thompson formula for oblique crossed cylinder and observ...

Abstract In 1998, Hu and Liu developed a strongly polynomial algorithm for solving the inverse arborescence problem that aims at minimally modifying given cost-function on edge-set of digraph D so an input spanning becomes cheapest one. this note, we develop conceptually simpler along with new min–max formula minimum modification cost-function. The approach is based link to theorem simple (two-...

In clinical practice the glomerular filtration rate (GFR) is estimated from serum creatinine-based equations like the Cockcroft-Gault formula (C&G) and Modification of Diet in Renal Disease formula (MDRD). Recently, serum cystatin C-based equations, the newer creatinine formula (The Chronic Kidney Disease Epidemiology Collaboration formula (CKD-EPI)), and equation that use both serum creatinine...

We generalize the generating formula for plane partitions known as MacMahon’s formula as well as its analog for strict plane partitions. We give a 2-parameter generalization of these formulas related to Macdonald’s symmetric functions. The formula is especially simple in the Hall-Littlewood case. We also give a bijective proof of the analog of MacMahon’s formula for strict plane partitions.

Three-factor interaction for the two-level, three-level, and four-level factorial designs was studied. A new technique and formula based on the coefficients of orthogonal polynomial contrast were proposed to calculate the effect of the three-factor interaction The results show that the proposed technique was in agreement with the least squares method. The advantages of the new technique are 1) ...

In this note, we prove a quantization formula for singular reductions. The main result is obtained as a simple application of an extended quantization formula proved in [TZ2].

We combine the parametric Barvinok algorithm with a generation algorithm for a finite list of suitably chosen discrete sub-cases on the enumeration of complete simple games, i. e. a special subclass of monotone Boolean functions. Recently, Freixas et al. have proven an enumeration formula for complete simple games with two types of voters. We will provide a shorter proof and an enumeration form...