21 research outputs found
Realizations of slice hyperholomorphic generalized contractive and positive functions
We introduce generalized Schur functions and generalized positive functions
in setting of slice hyperholomorphic functions and study their realizations in
terms of associated reproducing kernel Pontryagin spacesComment: Revised version,to appear in the Milan Journal of Mathematic
Exact value of 3 color weak Rado number
For integers k, n, c with k, n ≥ 1 and c ≥ 0, the n color weak Rado number
W Rk(n, c) is defined as the least integer N, if it exists, such that for every n coloring of the set {1, 2, ..., N}, there exists a monochromatic solution in that set
to the equation x1 + x2 + ... + xk + c = xk+1, such that xi = xj when i = j. If no
such N exists, then W Rk(n, c) is defined as infinite.
In this work, we consider the main issue regarding the 3 color weak Rado number
for the equation x1 + x2 + c = x3 and the exact value of the W R2(3, c) = 13c + 22
is established
Classification of Argyres-Douglas theories from M5 branes
We obtain a large class of new 4d Argyres-Douglas theories by classifying
irregular punctures for the 6d (2,0) superconformal theory of ADE type on a
sphere. Along the way, we identify the connection between the Hitchin system
and three-fold singularity descriptions of the same Argyres-Douglas theory.
Other constructions such as taking degeneration limits of the irregular
puncture, adding an extra regular puncture, and introducing outer-automorphism
twists are also discussed. Later we investigate various features of these
theories including their Coulomb branch spectrum and central charges.Comment: 35 pages, 9 tables, 6 figures. v2: minor correction
Totally Multicolored Rado Numbers For the Equation x_1 + x_2 + x_3 + ... + x_(m−1) = x_m
A set is called Totally Multicolored (TMC) if no elements in the set are colored the same. For all natural numbers t, m, let R(t, m) be the least natural number n such that for every t-coloring of the set {1, 2, 3, ..., R(t, m)} there exist a solution set {x_1, x_2, . . ., x_m} to L(m), x_1 + x_2 + x_3 + ... + x_(m−1) = x_m such that x_i does not equal x_j for all i that does not equal j, that avoids being Totally Multicolored. This paper shows a function to find R(t,m) for any t greater than or equal to 1 and m greater than or equal to 3. See the abstract in the text for the function that gives R(t,m)
Anti-van der Waerden Numbers of Graph Products with Trees
Given a graph , an exact -coloring of is a surjective function
. An arithmetic progression in of length with
common difference is a set of vertices such that
for . An arithmetic progression is rainbow
if all of the vertices are colored distinctly. The fewest number of colors that
guarantees a rainbow arithmetic progression of length three is called the
anti-van der Waerden number of and is denoted . It is known that
. Here we determine exact values for some trees and , determine for some trees
, and determine for some graphs and .Comment: 20 pages, 3 figure
Log-biharmonicity and a Jensen formula in the space of quaternions
Given a complex meromorphic function, it is well defined its Riesz measure in
terms of the laplacian of the logarithm of its modulus. Moreover, related to
this tool, it is possible to prove the celebrated Jensen formula. In the
present paper, using among the other things the fundamental solution for the
bilaplacian, we introduce a possible generalization of these two concepts in
the space of quaternions, obtaining new interesting Riesz measures and global
(i.e. four dimensional), Jensen formulas.Comment: Final Version. To appear on Annales Academiae Scientiarum Fennicae
Mathematica, Volume 44 (2019