What exactly is Takeuchi Yoshimi's logic of Asian resistance?

Literary Critic and Sinologist, Takeuchi Yoshimi, provides post-colonial and decolonial studies a logic of resistance that seeks to destabilize the colonialist projects of Western modernity without repeating its structural logic. In this regard, Takeuchi's logic of resistance functions as a dialectical lens into the “emancipatory traps” of Western modernity that frame the victim–victimizer paradox by turning negativity into a method of generating heuristic possibilities. But in this pursuit to look for alternative sites for mining theoretical possibilities, Takeuchi returns to the origins of Chinese modernity for imagining a proper logic of Asian resistance, that which could be deployed as a resource for negating the imperial gestures of modernist thought while affirming the positive kernel of the Enlightenment with the hope of bringing forth a global world that is continuously transformed by the cultural particulars themselves. The goal of this article is to further elucidate Takeuchi's logic of Asian resistance and to discuss how this logic can be read as having the potential to correct Nishida Kitarō's and the Kyoto School's failed attempt to overcome modernity.

Some Aspects of Positive Kernel Method of Quantization

We discuss various aspects of the positive kernel method of quantization of the one-parameter groups $$\tau _t \in \text{ Aut }(P,\vartheta )$$ τ t ∈ Aut ( P , ϑ ) of automorphisms of a G-principal bundle $$P(G,\pi ,M)$$ P ( G , π , M ) with a fixed connection form $$\vartheta $$ ϑ on its total space P. We show that the generator $${\hat{F}}$$ F ^ of the unitary flow $$U_t = e^{it {\hat{F}}}$$ U t = e i t F ^ being the quantization of $$\tau _t $$ τ t is realized by a generalized Kirillov–Kostant–Souriau operator whose domain consists of sections of some vector bundle over M, which are defined by a suitable positive kernel. This method of quantization applied to the case when $$G=\hbox {GL}(N,{\mathbb {C}})$$ G = GL ( N , C ) and M is a non-compact Riemann surface leads to quantization of the arbitrary holomorphic flow $$\tau _t^{\mathrm{hol}} \in \text{ Aut }(P,\vartheta )$$ τ t hol ∈ Aut ( P , ϑ ) . For the above case, we present the integral decompositions of the positive kernels on $$P\times P$$ P × P invariant with respect to the flows $$\tau _t^{\mathrm{hol}}$$ τ t hol in terms of the spectral measure of $${\hat{F}}$$ F ^ . These decompositions generalize the ones given by Bochner’s Theorem for the positive kernels on $${\mathbb {C}} \times {\mathbb {C}}$$ C × C invariant with respect to the one-parameter groups of translations of complex plane.

On regularity and stability for a class of nonlocal evolution equations with nonlinear perturbations

<p style='text-indent:20px;'>We study a class of nonlocal partial differential equations with nonlinear perturbations, which is a general model for some equations arose from fluid dynamics. Our aim is to analyze some sufficient conditions ensuring the global solvability, regularity and stability of solutions. Our analysis is based on the theory of completely positive kernel functions, local estimates and a new Gronwall type inequality.</p>

Halfspaces minimise nonlocal perimeter: a proof via calibrations

We consider a nonlocal functional $$J_K$$ J K that may be regarded as a nonlocal version of the total variation. More precisely, for any measurable function $$u:\mathbb {R}^d\rightarrow \mathbb {R}$$ u : R d → R , we define $$J_K(u)$$ J K ( u ) as the integral of weighted differences of u. The weight is encoded by a positive kernel K, possibly singular in the origin. We study the minimisation of this energy under prescribed boundary conditions, and we introduce a notion of calibration suited for this nonlocal problem. Our first result shows that the existence of a calibration is a sufficient condition for a function to be a minimiser. As an application of this criterion, we prove that halfspaces are the unique minimisers of $$J_K$$ J K in a ball, provided they are admissible competitors. Finally, we outline how to exploit the optimality of hyperplanes to recover a $$\varGamma $$ Γ -convergence result concerning the scaling limit of $$J_K$$ J K .

Quasigeostrophic Equations for Fractional Powers of Infinitesimal Generators

In this paper we treat the following partial differential equation, the quasigeostrophic equation: ∂/∂t+u·∇f=-σ-Aαf, 0≤α≤1, where (A,D(A)) is the infinitesimal generator of a convolution C0-semigroup of positive kernel on Lp(Rn), with 1≤p<∞. Firstly, we give remarkable pointwise and integral inequalities involving the fractional powers (-A)α for 0≤α≤1. We use these estimates to obtain Lp-decayment of solutions of the above quasigeostrophic equation. These results extend the case of fractional derivatives (taking A=Δ, the Laplacian), which has been studied in the literature.

On the asymptotic behaviour of nonlocal perimeters

We study a class of integral functionals known as nonlocal perimeters, which, intuitively, express a weighted interaction between a set and its complement. The weight is provided by a positive kernel K, which might be singular. In the first part of the paper, we show that these functionals are indeed perimeters in a generalised sense that has been recently introduced by A. Chambolle et al. [Archiv. Rational Mech. Anal. 218 (2015) 1263–1329]. Also, we establish existence of minimisers for the corresponding Plateau’s problem and, when K is radial and strictly decreasing, we prove that halfspaces are minimisers if we prescribe “flat” boundary conditions. A Γ-convergence result is discussed in the second part of the work. We study the limiting behaviour of the nonlocal perimeters associated with certain rescalings of a given kernel that has faster-than-L1 decay at infinity and we show that the Γ-limit is the classical perimeter, up to a multiplicative constant that we compute explicitly.