Related papers: Rigidity method for automorphic forms over functio…
We explore the rigidity of generic frameworks in 3-dimensions whose underlying graph is close to being planar. Specifically we consider apex graphs, edge-apex graphs and their variants and prove independence results in the generic…
The goal of these lecture notes is to present in a unified way various models for the dynamics of aligning self-propelled rigid bodies at different scales and the links between them. The models and methods are inspired from [12,13], but, in…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
The availability of a reliable bound on an integral involving the square of the modulus of a form factor on the unitarity cut allows one to constrain the form factor at points inside the analyticity domain and its shape parameters, and also…
For any even natural number $r \ge 2$, we construct an irreducible rigid non-cohomologically rigid complex local system of rank $r$ on a smooth projective variety depending on $r$. For $r=2$, we construct an irreducible rigid…
Suppose $G$ is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on $G$ which have topological structures. In this paper, our attempt is to assign lattice structures on them. More…
In this thesis we explore natural procedures through which topological structure can be constructed from specific semigroups. We will do this in two ways: 1) we equip the semigroup object itself with a topological structure, and 2) we find…
Nonholonomic systems are variational models commonly used for mechanical systems with ideal no-slip constraints. This note provides a differential-geometric derivation of the nonholonomic equations of motion for an arbitrary rigid body…
We study the simplicial order complexes obtained from free modules over finite local rings. These complexes arise naturally as geodesic spheres in Bruhat-Tits buildings over non-archimedean local fields. We establish two forms of rigidity,…
A rigid automorphism of a linking system is an automorphism which restricts to the identity on the Sylow subgroup. A rigid inner automorphism is conjugation by an element in the center of the Sylow subgroup. At odd primes, it is known that…
In this survey, we systematically summarize the current literature on studies that apply reinforcement learning (RL) to the motion planning and control of autonomous vehicles. Many existing contributions can be attributed to the pipeline…
New geometric structures that relate the lagrangian and hamiltonian formalisms defined upon a singular lagrangian are presented. Several vector fields are constructed in velocity space that give new and precise answers to several topics…
Nonlocal gravity models are constructed to explain the current acceleration of the universe. These models are inspired by the infrared correction appearing in Einstein Hilbert action. Here we develop the Hamiltonian formalism of a nonlocal…
We give examples of cohomological automorphic forms for unitary groups which are $p$-adically rigid.
We use a method of Buzzard to study p-adic families of different types of modular forms - classical, over imaginary quadratic fields and totally real fields. In the case of totally real fields of even degree, we get local constancy of…
We define and study slider-pinning rigidity, giving a complete combinatorial characterization. This is done via direction-slider networks, which are a generalization of Whiteley's direction networks.
We establish Bochner-type formulas for operators related to $CR$ automorphisms and spherical $CR$ structures. From such formulas, we draw conclusions about rigidity by making assumptions on the Tanaka-Webster curvature and torsion.
In this work we use the deformation procedure and explore the route to obtain distinct field theory models that present similar stability potentials. Starting from systems that interact polynomially or hyperbolically, we use a deformation…
A family of real Hamiltonian forms (RHF) for the special class of affine 1+1 - dimensional Toda field theories is constructed. Thus the method, proposed in [Mikhailov;1981] for systems with finite number of degrees of freedom is generalized…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…