Let $C$ be a smooth complex projective curve and $G$ connected reductive group. We prove that if the center $Z(G)$ of is disconnected, then Kirwan map $H^*\big(\operatorname{Bun}(G,C),\mathbb{Q}\big)\rightarrow H^*\big(\mathcal{M}_{\operatorname{Higgs}}^{\operatorname{ss}},\mathbb{Q}\big)$ from cohomology moduli stack $G$-bundles to semistable $G$-Higgs bundles, fails surjective: more precisely...

A bicommutant category is a higher categorical analog of von Neumann algebra. We study the categories which arise as commutant $${\mathcal {C}}'$$ fully faithful representation {C}}\rightarrow \textrm{Bim}(R)$$ unitary fusion {C}}$$ . Using results Izumi, Popa, and Tomatsu about existence uniqueness representations (multi)fusion categories, we prove that if {D}}$$ are Morita equivalent then the...

The big bang-big crunch (BB-BC) algorithm is a popular metaheuristic optimization technique proposed based on one of the theories for the evolution of the universe. The algorithm utilizes a two-phase search mechanism: big-bang phase and big-crunch phase. In the big-bang phase the concept of energy dissipation is considered to produce disorder and randomness in the candidate population while in ...

this article presents the application of two algorithms: heuristic big bang-big crunch (hbb-bc) and a heuristic particle swarm ant colony optimization (hpsaco) to discrete optimization of reinforced concrete planar frames subject to combinations of gravity and lateral loads based on aci 318-08 code. the objective function is the total cost of the frame which includes the cost of concrete, formw...

The blades of a wind turbine have the most important job of any wind turbine component; they must capture the wind and convert it into useable mechanical energy. The objective of this work is to determine the mechanical power of single big C-section of vertical wind turbine for wind car in a two-dimensional model. The wind car has a vertical axis with 3 single big C-section blades mounted at an...

The Zygmund sums of a function $f\in L_{1}$ are trigonometric polynomials the form $$Z^{s}_{n-1}(f;t):=\frac{a_{0}}{2}+\sum_{k=1}^{n-1}\Big(1-\big(\frac{k}{n}\big)^{s}\Big) \big(a_{k}(f)\cos kt+b_{k}(f)\sin kt\big), s>0,$$ where $a_{k}(f)$ and $b_{k}(f)$ Fourier coefficients $f$. We establish exact-order estimates uniform approximations by $Z^{s}_{n-1}$ $2\pi$-periodic continuous functions f...

This paper is concerned with the critical sharp traveling wave for doubly nonlinear diffusion equation time delay, where degenerate defined by $\Big(\big|(u^m)_x\big|^{p-2}(u^m)_x\Big)_x$ $m>0$ and $p>1$. The proved to admit a unique type case $m(p-1)>1$, so-called slow-diffusion case. associated minimal speed $c^*(m,p,r)$ monotonically increasing, satisfies $c^*(m,p,r)<c^*(m,p,0)$ any delay $r...

Given a big divisor D on a normal complex projective variety X , we show that the restricted volume of D along a very general complete-intersection curve C ⊂ X can be read off from the Okounkov body of D with respect to an admissible flag containing C. From this we deduce that if two big divisors D1 and D2 on X have the same Okounkov body with respect to every admissible flag, then D1 and D2 ar...

..................................................................................................................... 1 A. Two Digital Research Legs: Empirical Induction and Deductive Models ..... 2 B. Big Data for Development ........................................................................ 4 B1. CHARACTERISTICS OF BIG DATA...................................................................