Related papers: A Young-type integration on self-similar sets in i…
In this paper, we prove a result similar to results of Itoh and Hong-Ulrich, proving that integral closure of an ideal is compatible with specialization by a general element of that ideal for ideals of height at least two in a large class…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…
For nonautonomous, nonuniformly elliptic integrals with so-called $(p,q)$-growth conditions, we show a general interpolation property allowing to get basic higher integrability results for H\"older continuous minimizers under improved…
We consider a renewal-like recursion and prove that the solution is polynomially decaying asymptotically under suitable conditions. We prove similar results for the corresponding integral equation. In both cases coefficients and functions…
These lectures give a basic introduction to $\mathcal{N}=4$ SYM theory and the integrability of its planar spectral problem as seen from the perspective of a recent development, namely the application of integrability techniques in the…
We take under consideration Young measures with densities. The notion of density of a Young measure is introduced and illustrated with examples. It is proved that the density of a Young measure is weakly sequentially closed set. In the case…
In this letter we establish Yangian symmetry of planar N=4 super-Yang-Mills theory. We prove that the classical equations of motion of the model close onto themselves under the action of Yangian generators. Moreover we propose an off-shell…
We give a brief overview of the Yangian symmetry of Feynman integrals. After a short introduction to the Yangian and integrability, we motivate the emergence of integrable structures for Feynman integrals via the fishnet limit of AdS/CFT.…
We show that keeping only the topologically trivial contribution to the average of a class function on U(N) amounts to integrating over its algebra. The goal is reached first by decompactifying an expansion over the instanton basis and then…
We show that for ideals primary to a maximal ideal in a normal domain of finite type over the complex numbers, its tight closure is contained inside the continuous closure.
Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.
A little-known and highly economical characterization of the real interval [0, 1], essentially due to Freyd, states that the interval is homeomorphic to two copies of itself glued end to end, and, in a precise sense, is universal as such.…
The Sinc quadrature and the Sinc indefinite integration are approximation formulas for definite integration and indefinite integration, respectively, which can be applied on any interval by using an appropriate variable transformation.…
We propose and implement an approach to inference in linear instrumental variables models which is simultaneously robust and computationally tractable. Inference is based on self-normalization of sample moment conditions, and allows for…
The method of exhaustion is generalized to a simple formula that can be used to integrate functions under very general conditions, provided that the integral exists. Both a geometric proof (following the usual procedure for the method of…
For a Riemann integrable function on an interval and for a point therein,we define 'Fourier series at the point on the interval' and bring out how and when the function element becomes expressible as Fourier series.In this process,we also…
We extend conformal inference to general settings that allow for time series data. Our proposal is developed as a randomization method and accounts for potential serial dependence by including block structures in the permutation scheme. As…
We show that for constant rank partial differential operators $\mathscr{A}$, generalized Young measures generated by sequences of $\mathscr{A}$-free measures can be characterized by duality with $\mathscr{A}$-quasiconvex integrands of…
Given a function $f\in C(\mathbb{R}^d)$ of linear growth, we give a new way of representing accumulation points of \begin{equation} \int_\Omega f(v_i(z))d\mu(z), \end{equation} where $\mu\in \mathcal{M}^+(\Omega)$, and $(v_i)_{i\in…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…