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In this paper we apply the tools developed in [4] in order to present some consequences of the study of UMP algebras and the ramifications graph of a monomial bound quiver algebra. In particular, we prove that every weakly connected component of the ramifications graph of a UMP monomial algebra is unilaterally connected. Furthermore, we use this characterization to show that, in the case of quadratic monomial algebras, the class of UMP algebras coincides with the class of special multiserial algebras., Comment: 10 pages. arXiv admin note: text overlap with arXiv:2309.11624

The class of UMP algebras arises in several classification problems in the context of derived categories of finite-dimensional algebras. In this paper we define the class of UMP algebras and develop algebraic combinatorics tools in order to present a characterization of this class of algebras which are locally monomial (see Definition 4.1) and special multiserial algebras. Among other things, we describe the ramifications graph of symmetric special biserial algebras and we classify which of them are UMP algebras in terms of their bound quivers and their associated Brauer graphs., Comment: 18 pages, Section 5-1 included

Magnetic systems can be described by the classical Landau-Lifshitz (LL) equation or the fully quantum open Heisenberg model. Using the Lindblad master equation and the mean-field approximation, we demonstrate that the open Heisenberg model is reduced to a generalized LL equation. The open dynamic is modeled using spin-boson interactions with a common bosonic reservoir at thermal equilibrium. By tracing out the bosonic degrees of freedom, we obtain two different decoherence mechanisms: on-site dissipation and an effective spin-spin interaction mediated by bosons. Using our approach, we perform hysteresis calculations, closely connected with the Stoner-Wohlfarth theory. We compare the exact numerical master equation and the mean-field model, revealing the role of correlations originated by non-local interactions. Our work opens new horizons for the study of the LL dynamics from an open quantum formalism., Comment: 11 pages, 6 figures

In this paper we develop combinatorial techniques for the case of string algebras with the aim to give a characterization of string complexes with infinite minimal projective resolution. These complexes will be called \textit{periodic string complexes}. As a consequence of this characterization, we give two important applications. The first one, is a sufficient condition for a string algebra to have infinite global dimension. In the second one, we exhibit a class of indecomposable objects in the derived category for a special case of string algebras. Every construction, concept and consequence in this paper is followed by some illustrative examples., Comment: arXiv admin note: substantial text overlap with arXiv:1910.04012

We give a combinatorial description of a family of indecomposable objects in the bounded derived categories of a new class of algebras: string almost gentle algebras. These indecomposable objects are, up to isomorphism, the string and band complexes introduced by V. Bekkert and H. Merklen. With this description, we give a necessary and sufficient condition for a given string complex to have infinite minimal projective resolution and we extend this condition for the case of string algebras. Using this characterization we establish a sufficient condition for a string almost gentle algebra (or a string algebra) to have infinite global dimension., Comment: We have added new examples. Also, we have renewed some proofs and corrected minor typos

Peano Arithmetic is known to be provably equivalent to reflection over Elementary Arithmetic. We prove a characterization of Predicative Analysis in the guise of ATR0 in terms of stronger reflection principles.

In the generalized Russian cards problem, the three players Alice, Bob and Cath draw a,b and c cards, respectively, from a deck of a+b+c cards. Players only know their own cards and what the deck of cards is. Alice and Bob are then required to communicate their hand of cards to each other by way of public messages. The communication is said to be safe if Cath does not learn the ownership of any specific card; in this paper we consider a strengthened notion of safety introduced by Swanson and Stinson which we call k-safety. An elegant solution by Atkinson views the cards as points in a finite projective plane. We propose a general solution in the spirit of Atkinson's, although based on finite vector spaces rather than projective planes, and call it the `geometric protocol'. Given arbitrary c,k>0, this protocol gives an informative and k-safe solution to the generalized Russian cards problem for infinitely many values of (a,b,c) with b=O(ac). This improves on the collection of parameters for which solutions are known. In particular, it is the first solution which guarantees $k$-safety when Cath has more than one card.

We investigate the effect of coupling (intensity and nature), applied field, and anisotropy on the spin dynamics of a multi-layer system composed of a hard magnetic slab coupled to a soft magnetic slab through a nonmagnetic spacer. The soft slab is modeled as a stack of several atomic layers while the hard layer, of a different material, is either considered as a pinned macroscopic magnetic moment or as an atomic multi-layer system. We compute the magnetization profile and hysteresis loop of the multi-layer system by solving the Landau-Lifshitz equations for the net magnetic moment of each (atomic) layer. We study the competition between the intra-layer anisotropy and exchange interaction, applied magnetic field, and the inter-slab exchange, dipolar or Dzyaloshinski-Moriya interaction. Comparing the effects on the magnetization profile of the three couplings shows that despite the strong effect of the exchange coupling, the dipolar and Dzyaloshinski-Moriya interactions induce a slight (but non negligible) deviation in either the polar or azimuthal direction thus providing more degrees of freedom for adjusting the spin configuration in the multi-layer system.

In the generalized Russian cards problem, Alice, Bob and Cath draw $a$, $b$ and $c$ cards, respectively, from a deck of size $a+b+c$. Alice and Bob must then communicate their entire hand to each other, without Cath learning the owner of a single card she does not hold. Unlike many traditional problems in cryptography, however, they are not allowed to encode or hide the messages they exchange from Cath. The problem is then to find methods through which they can achieve this. We propose a general four-step solution based on finite vector spaces, and call it the "colouring protocol", as it involves colourings of lines. Our main results show that the colouring protocol may be used to solve the generalized Russian cards problem in cases where $a$ is a power of a prime, $c=O(a^2)$ and $b=O(c^2)$. This improves substantially on the set of parameters for which solutions are known to exist; in particular, it had not been shown previously that the problem could be solved in cases where the eavesdropper has more cards than one of the communicating players.

Consider three players Alice, Bob and Cath who hold a, b and c cards, respectively, from a deck of d=a+b+c cards. The cards are all different and players only know their own cards. Suppose Alice and Bob wish to communicate their cards to each other without Cath learning whether Alice or Bob holds a specific card. Considering the cards as consecutive natural numbers 0,1,..., we investigate general conditions for when Alice or Bob can safely announce the sum of the cards they hold modulo an appropriately chosen integer. We demonstrate that this holds whenever a,b>2 and c=1. Because Cath holds a single card, this also implies that Alice and Bob will learn the card deal from the other player's announcement.