Related papers: The Intermediate Value Theorem for Linear Transfor…
We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…
Each family $\mathcal{M}$ of means has a natural, partial order (point-wise order), that is $M \le N$ iff $M(x) \le N(x)$ for all admissible $x$. In this setting we can introduce the notion of interval-type set (a subset $\mathcal{I}…
Many problems in optimization theory are strongly nonlinear in the traditional sense but possess a hidden linear structure over suitable idempotent semirings. After an overview of `Idempotent Mathematics' with an emphasis on matrix theory,…
Rademacher theorem asserts that Lipschitz continuous functions between Euclidean spaces are differentiable almost everywhere. In this work we extend this result to set-valued maps using an adequate notion of set-valued differentiability…
Recently, Keller and Pilpel conjectured that the influence of a monotone Boolean function does not decrease if we apply to it an invertible linear transformation. Our aim in this short note is to prove this conjecture.
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
In this paper, we have proved four theorems on the degree of approximation of continuous functions by matrix means of their Fourier series which is expressed in terms of the modulus of continuity and a non-negative mediate function.
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their…
This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this…
The work is devoted to the construction of a new type of intervals -- functional intervals. These intervals are built on the idea of expanding boundaries from numbers to functions. Functional intervals have shown themselves to be promising…
We define an integral of real-valued functions with respect to a measure that takes its values in the extended positive cone of a partially ordered vector space $E$. The monotone convergence theorem, Fatou's lemma, and the dominated…
Balancing square and rectangular tables by rotation has been a interesting way to illustrate the intermediate value theorem. The aim of this note is to show that the balancing act but with non-rectangular tables can be a nice application of…
Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…
In this paper, we prove a criterion for existence of continuous non constant eigenfunctions for interval exchange transformations, that is for non topologically weak mixing. We first construct, for any m>3, uniquely ergodic interval…
In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…
In this paper we assemble some results about the upper-semicontinuity and lower-semicontinuity of the feasible correspondence and the solution correspondence of linear programming problems allowing variability of all parameters of such…
Norm equivalences between a function and its Hankel transform are studied both in the context of weighted Lebesgue spaces with power weights, and in Lorentz spaces. Boas'-type results involving real-valued general monotone functions are…
We consider a monotone increasing operator in an ordered Banach space having $u_-$ and $u_+$ as a strong super- and subsolution, respectively. In contrast with the well studied case $u_+ < u_-$, we suppose that $u_- < u_+$. Under the…
The simplest way to obtain continuous interpolation between two points in high dimensional space is to draw a line between them. While previous works focused on the general connectivity between model parameters, we explored linear…
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.