Related papers: Designing plateaued Boolean functions in spectral …

We construct a class of bounded domains, on which the squeezing function is not uniformly bounded from below near a smooth and pseudoconvex boundary point.

Continuum normalization of echelle spectra is an important data analysis step that is difficult to automate. Polynomial fitting requires a reasonably high order model to follow the steep slope of the blaze function. However, in the presence…

The performance of optimization methods is often tied to the spectrum of the objective Hessian. Yet, conventional assumptions, such as smoothness, do often not enable us to make finely-grained convergence statements -- particularly not for…

Affine normal directions provide intrinsic affine-invariant descent directions derived from the geometry of level sets. Their practical use, however, has long been hindered by the need to evaluate third-order derivatives and invert tangent…

Submodular continuous functions are a category of (generally) non-convex/non-concave functions with a wide spectrum of applications. We characterize these functions and demonstrate that they can be maximized efficiently with approximation…

It has been an active research issue for many years to construct new bent functions. For $k$ odd with $\gcd(n, k)=1$, and $a\in\mathbb{F}_{3^n}^{*}$, the function $f(x)=Tr(ax^{\frac{3^k+1}{2}})$ is weakly regular bent over…

We define Schwartz functions, tempered functions and tempered distributions on (possibly singular) real algebraic varieties. We prove that all classical properties of these spaces, defined previously on affine spaces and on Nash manifolds,…

In the field of statistics, many kind of divergence functions have been studied as an amount which measures the discrepancy between two probability distributions. In the differential geometrical approach in statistics (information…

An important classification of permutations over $\mathbb{F}_2^m$, suitable for constructing Maiorana-McFarland bent functions on $\mathbb{F}_2^m \times \mathbb{F}_2^m$ with the unique $M$-subspace of maximal dimension, was recently…

In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…

For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…

This work characterizes the structure of third and forth order WENO weights by deducing data bounded condition on third order polynomial approximations. Using these conditions, non-linear weights are defined for third and fourth order data…

An affine factorable surface of the second kind in the three dimensional pseudo-Galilean space G13 is studied depending on the invariant theory and theory of differential equation. The first and second fundamental forms, Gaussian curvature…

We consider a class of inverse problems defined by a nonlinear map from parameter or model functions to the data. We assume that solutions exist. The space of model functions is a Banach space which is smooth and uniformly convex; however,…

We define and study classes of smooth functions which are less regular than Gevrey functions. To that end we introduce two-parameter dependent sequences which do not satisfy Komatsu's condition (M.2)', which implies stability under…

In this work, transverse shear warping functions for an equivalent single layer plate model are formulated from a variational approach. The part of the strain energy which involves the shear phenomenon is expressed in function of the…

There are two construction methods of designs from $(n,m)$-bent functions, known as translation and addition designs. In this paper we analyze, which equivalence relation for Boolean bent functions, i.e. $(n,1)$-bent functions, and…

In order to produce a low energy effective field theory from a string model, it is necessary to specify a vacuum state. In order that this vacuum be supersymmetric, it is well known that all field expectation values must be along so-called…

Shape restrictions on functional regression coefficients such as non-negativity, monotonicity, convexity or concavity are often available in the form of a prior knowledge or required to maintain a structural consistency in functional…

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…