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The correlation of odd electrons in graphene turns out to be significant so that the species should be attributed to correlated ones. This finding profoundly influences the computational strategy addressing it to multireference…
We study a versatile structurally favorable periodic $sp^2$-bonded carbon atomic planar sheet with $C_{4v}$ symmetry by means of the first-principles calculations. This carbon allotrope is composed of carbon octagons and squares with two…
A classification scheme of hadrons is proposed on the basis of the division algebra H of quaternions and an appropriate geometry. This scheme suggests strongly to understand flavour symmetry in another manner than from standard symmetry…
The rapid outbreaks of lethal viruses necessitate the development of novel antiviral substance. Besides the conventional antiviral substances, biocompatible nanomaterials also have significant potential in combating the virus at various…
Of the ``presolar particles'' extracted from carbonaceous chondrite dissolution residues, i.e. of those particles which show isotopic evidence of solidification in the neighborhood of other stars prior to the origin of our solar system, one…
We discuss the role and merits of symmetry methods for the analysis of biological systems. In particular, we consider systems of first order ordinary differential equations and provide a comprehensive review of the geometrical foundations…
Following Serre's initial work, a number of authors have considered twists of quadratic forms on a scheme Y by torsors of a finite group G, together with formulas for the Hasse-Witt invariants of the twisted form. In this paper we take the…
We consider a system of particles confined in a box $\La\subset\R^d$ interacting via a tempered and stable pair potential. We prove the validity of the cluster expansion for the canonical partition function in the high temperature - low…
We first exploit the physical condition satisfying the symmetry relation of the ``exact'' spin-resolved exchange correlation kernel based on the ``mixed scheme'' in soft magnetic layered systems. The conditions are derived and examined by…
Brane systems provide a large class of gauge theories that arise in string theory. This paper demonstrates how such brane systems fit with a somewhat exotic geometric object, called the affine Grassmannian. This gives a strong motivation to…
This paper deals with affine connections on real manifolds. We give a new characterization of flat affine connections on real manifolds by means of certain affine representations of the Lie group of automorphisms preserving the connection.…
Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low temperature phases of matter. In celebrated work,…
The introduction of a Flavour Symmetry can represent an interesting way in which one can try to find an answer to some intriguing problems in Flavour Physics, like the hierarchy between the fermion masses or the particular values of mixing…
We show that the assumption of non-zero topological susceptibility of the vacuum in a fermion-free version of a theory, such as gravity or QCD, suffices to conclude the following: Once N massless fermion flavors are added to the theory,…
Fullerenes are a particularly stable class of carbon molecules in the shape of a hollow sphere or ellipsoid that might be formed in the outflows of carbon stars. Once injected into the interstellar medium (ISM), these stable species survive…
Based on first-principles calculations we predict a peculiar growth process, where carbon adatoms adsorbed to graphene readily diffuse above room temperature and nucleate segments of linear carbon chains attached to graphene. These chains…
We demonstrate that exact supersymmetry can emerge in a purely fermionic system. This "supersymmetry without bosons" is unveiled by constructing a novel boson-fermion Dyson mapping from a fermion space to a space comprised of collective…
We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer…
An enumerative problem on a variety $V$ is usually solved by reduction to intersection theory in the cohomology of a compactification of $V$. However, if the problem is invariant under a "nice" group action on $V$ (so that $V$ is…
In this paper, we explore affine semigroup versions of the convex geometry theorems of Helly, Tverberg, and Caratheodory. Additionally, we develop a new theory of colored affine semigroups, where the semigroup generators each receive a…