Entanglement forging based variational algorithms leverage the bipartition of quantum systems for addressing ground-state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous potential basis stat ...
Countless aspects of touch and closeness have been questioned in an unprecedented way during the recent Covid epidemic. Social practices as banal as greetings were both reflexively and practically challenged and sometimes deeply altered, resulting in painf ...
Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...
Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups w ...
We determine the dimensions of Ext -groups between simple modules and dual generalized Verma modules in singular blocks of parabolic versions of category O for complex semisimple Lie algebras and affine Kac-Moody algebras. ...
Many problems in robotics are fundamentally problems of geometry, which have led to an increased research effort in geometric methods for robotics in recent years. The results were algorithms using the various frameworks of screw theory, Lie algebra, and d ...
Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is discussed to illustrate ...
Encouraging a modal shift from individual transportation to less polluting modes such as public transport, walking and cycling, is now a key recommendation of the UN to reach the goals set by the Paris Agreement. Achieving this ambitious goal requires a de ...
We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting complexes for standard objects and simple objects. For certain categories of representations of complex simple Lie ...
We prove some new cases of the Grothendieck-Serre conjecture for classical groups. This is based on a new construction of the Gersten-Witt complex for Witt groups of Azumaya algebras with involution on regular semilocal rings, with explicit second residue ...
A new miniaturized micro sequential injection coupled with the lab-on-valve (mu SIA-LOV) technique was full-blown to perform inhibitory studies on dihydrofolate reductase (DHFR). The system was used to evaluate the DHFR inhibition activity of metal-based a ...
In the class of Sobolev vector fields in R-n of bounded divergence, for which the theory of DiPerna and Lions provides a well defined notion of flow, we characterize the vector fields whose flow commutes in terms of the Lie bracket and of a regularity cond ...
In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of b-symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864-896, we prove a slice theorem for Lie group a ...
The nearby elliptical galaxy Centaurus A (Cen A) is surrounded by a flattened system of dwarf satellite galaxies with coherent motions. Using a novel Bayesian approach, we measured the mean rotation velocity nu(rot) and velocity dispersion sigma(int) of th ...
We study correlation functions involving generalized ANEC operators of the form integral dx-x-n+2T--x -> in four dimensions. We compute two, three, and ...
We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when G is a connected reductive complex algebraic group with simply-connected derived subgroup, two conjugacy classes ...
Let u(q)(g) be the small quantum group associated with a complex semisimple Lie algebra g and a primitive root of unity q, satisfying certain restrictions. We establish the equivalence between three different actions of g on the center of u(q)(g) and on th ...
We start this short note by introducing two remarkable mathematical objects: the E8E8 root lattice Lambda8Lambda8 in 8-dimensional Euclidean space and the Leech lattice Lambda24Lambda24 in 24-dimensional space. These two lattices stand out among their lat ...
The development of radical-based remote C(sp3)-H functionalizations of redox-active alcohol derivatives, oxidative cycloaddition and rearrangement transformations under visible light photocatalysis constitute the basis of this thesis.
The first chapter des ...
We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence ...
