In this talk we will report on few results of discrete physics on the fuzzy sphere . In particular non-trivial field configurations such as monopoles and solitons are constructed on fuzzy S using the language of K-theory , i.e projectors . As we will show , these configurations are intrinsically finite dimensional matrix models . The corresponding monopole charges and soliton winding numbers ar...

The notion of mixed mock modular forms was recently introduced by Don Zagier. We show that certain solutions of Kaneko Zagier differential equation constitute simple yet non-trivial examples of this notion. That allows us to address a question posed by Kaneko and Koike on the (non)-modularity of these solutions.

A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential equations with two fixed time lags is mainly studied for its dependency on varying connection stre...

For an integer d?2, a family F of sets is d-wise intersecting if for any distinct A1,A2,…,Ad?F, A1?A2?…?Ad??, and non-trivial ?A?FA=?. Hilton Milner conjectured that k?d?2 large enough n, the extremal (i.e. largest) k-element subsets [n] is, up to isomorphism, one following two families:A(k,d)={A?([n]k):|A?[d+1]|?d}H(k,d)={A?([n]k):[d?1]?A,A?[d,k+1]??}?{[k+1]?{i}:i?[d?1]}. The celebrated Hilton...

A non-trivial super black hole solution is considered as representing a combined model of the Kerr spinning particle and superparticle. Treatment is based on the broken N=2 supersymmetry in su-pergravity in analogue with Deser-Zumino model of broken su-persymmetry in N=1 supergravity. There appears a non-linear realization of broken supersymmetry, which is very specific for the Kerr geometry an...

We study the problem of chaos in temperature in some mean-field spin-glass models by means of a replica computation over a model of coupled systems. We propose a set of solutions of the saddle point equations which are intrinsically non-chaotic and solve a general problem regarding the consistency of their structure. These solutions are relevant in the case of uncoupled systems too, therefore t...

‎Here‎, ‎we investigate a conjecture posed by Amiri and Ariannejad claiming‎ ‎that if every maximal subfield of a division ring $D$ has trivial normalizer‎, ‎then $D$ is commutative‎. ‎Using Amitsur classification of‎ ‎finite subgroups of division rings‎, ‎it is essentially shown that if‎ ‎$D$ is finite dimensional over its center then it contains a maximal‎ ‎subfield with non-trivial normalize...

We show that a previous paper of Freund describing a solution to the Seiberg– Witten equations has a sign error rendering it a solution to a related but different set of equations. The non-L 2 nature of Freund's solution is discussed and clarified and we also construct a whole class of solutions to the Seiberg–Witten equations. § 1. Introduction With the introduction of the Seiberg–Witten equat...