Related papers: A Jacobson Radical Decomposition of the Fano-Snowf…
Given a finite associative ring with unity, $R$, any free (left) cyclic submodule (FCS) generated by a $uni$modular ($n+1$)-tuple of elements of $R$ represents a point of the $n$-dimensional projective space over $R$. Suppose that $R$ also…
Given a ring of ternions $R$, i. e., a ring isomorphic to that of upper triangular $2\times 2$ matrices with entries from an arbitrary commutative field $F$, a complete classification is performed of the vectors from the free left…
Let $\frak{n}$ be a square-free ideal of $\mathbb{F}_q[T]$. We study the rational torsion subgroup of the Jacobian variety $J_0(\frak{n})$ of the Drinfeld modular curve $X_0(\frak{n})$. We prove that for any prime number $\ell$ not dividing…
T.Kishimoto raised the problem to classify all compactifications of contractible affine 3-folds into smooth Fano 3-folds with second Betti number two and classified such compactifications whose log canonical divisors are not nef. In this…
We construct Fano threefolds with very ample anti-canonical bundle and Picard rank greater than one from cracked polytopes - polytopes whose intersection with a complete fan forms a set of unimodular polytopes - using Laurent inversion; a…
A left and right noetherian semiperfect ring R is known to be indecomposable if and only if its factor by the second power of Jacobson radical is. This characterisation is used to study simple R-modules in terms of their Ext groups. It is…
We investigate projective covers of cyclically presented modules, characterizing the rings over which every cyclically presented module has a projective cover as the rings $R$ that are Von Neumann regular modulo their Jacobson radical…
Fan-spine magnetic structure, as a fundamental three-dimensional topology in magnetic reconnection theory, plays a crucial role in producing solar jets. However, how fan-spine configurations form in the solar atmosphere remains elusive.…
We use fragmenting jet functions (FJFs) in the context of quarkonia to study the production channels predicted by NRQCD (3S_1^(1), 3S_1^(8), 1S_0^(8), 3P_J^(8)). We choose a set of FJFs that give the probability to find a quarkonium with a…
It is shown that the layered antiferromagnetic order in stoechiometric LaMnO_3 cannot be understood purely from electronic interactions. On the contrary, it mainly results from strong cooperative Jahn-Teller deformations. Those involve a…
The electronic structure and magnetism in the sodium nickelate NaNiO_2 in the low-temperature phase is studied from density-functional calculations using the linear muffin-tin orbitals method. An antiferromagnetic solution with a magnetic…
We report on high-temperature electron spin resonance studies of a detwinned LaMnO$_3$ single crystal across the Jahn-Teller transition at $T_{\rm JT}$ = 750 K. The anisotropy of the linewidth and g-factor reflects the local Jahn-Teller…
The appearance of scalar/moduli fields in the early universe, as motivated by string theory, naturally leads to non-thermal "moduli cosmology". Such cosmology provides a consistent framework where the generation of radiation, baryons, and…
The evolution of inclination angle and precession damping of radio pulsars is considered. It is assumed that the neutron star consists of 3 "freely" rotating components: the crust and two core components, one of which contains pinned…
We report an in-plane optical spectroscopy study on the iron-selenide superconductor K$_{0.75}$Fe$_{1.75}$Se$_2$. The measurement revealed the development of a sharp reflectance edge below T$_c$ at frequency much smaller than the…
We discuss interrelations between: Cohn localizations of full square matrices; a Leavitt localization of a row; and the Jacobson quasi-inverses of quasi-regular elements. The latter Jacobson localizations appear naturally and easily in…
We study a three-components fermionic gas loaded in a one-dimensional optical trap at half-filling. We find that the system is fully gapped and may order into 8 possible phases: four 2$k_F$ atomic density wave and spin-Peierls phases with…
The free Jacobi process is the radial part of the compression of the free unitary Brownian motion by two free orthogonal projections in a non commutative probability space. In this paper, we derive spectral properties of the free Jacobi…
We consider Cremona transformations of the complex projective space of dimension 3 which factorize as a product of at most two elementary links of type II, without small contractions, connecting two Fano 3-folds. We show that there are…
We discuss the ground state of the spin-orbital model for spin-one ions with partially filled $t_{2g}$ levels on a honeycomb lattice. We find that the orbital degrees of freedom induce a spontaneous dimerization of spins and drive them into…