We investigate the finite-size scaling of entanglement gap in one dimensional long-range quantum spherical model (QSM). focus on weak QSM, for which thermodynamic limit is well-defined. This exhibits a continuous phase transition, separating paramagnetic from ferromagnet phase. The universality class transition depends exponent $\alpha$. show that finite phase, and it vanishes ferromagnetic In ...

There have been intense debates about the decomposition of regional diversity (gamma) into its within-community component (alpha) and between-community component (beta). Although a recent Ecology Forum achieved consensus in the use of "numbers equivalents" (Hill numbers) as the proper choice of diversity measure, three related major issues were still left unresolved. (1) What is the precise mea...

We study the dynamics of a version of the batch minority game, with random external information and with different types of inhomogeneous decision noise (additive and multiplicative), using generating functional techniques à la De Dominicis. The control parameters in this model are the ratio alpha=p/N of the number p of possible values for the external information over the number N of trading a...

We introduce and analyze a novel type of coalescent processes called cross-multiplicative that models system with two types particles, $A$ $B$. The bonds are formed only between the pairs particles opposite same rate for each bond, producing connected components made both types. solve Smoluchowski coagulation equations obtained as hydrodynamic limit corresponding Marcus-Lushnikov process. estab...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...

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Write $$\mathrm {ord}_p(\cdot )$$ for the multiplicative order in $${\mathbb {F}}_p^{\times }$$ . Recently, Matthew Just and second author investigated problem of classifying pairs $$\alpha , \beta \in {\mathbb {Q}}^{\times }\setminus \{\pm 1\}$$ which {ord}_p(\alpha ) > \mathrm {ord}_p(\beta holds infinitely many primes p. They called such order-dominant. We describe an easily-checkable suffic...

There are several kinds of hyperrings, for example, Krasnerhyperrings, multiplicative hyperring, general hyperrings and$H_v$-rings. In a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf Keywords:} multiplic...

Motivated by reformulating Yangian invariants in planar ${\cal N}=4$ SYM directly as $d\log$ forms on momentum-twistor space, we propose a purely algebraic problem of determining the arguments $d\log$'s, which call "letters", for any invariant. These are functions momentum twistors $Z$'s, given positive coordinates $\alpha$'s parametrizations matrix $C(\alpha)$, evaluated support polynomial equ...