Related papers: Jet schemes, arc spaces and the Nash problem
This paper studies the singularities of jet schemes of homogeneous hypersurfaces of general type. We obtain the condition of the degree and the dimension for the singularities of the jet schemes to be of dense $F$-regular type. This…
I discuss recent developments in the field of relativistic jets in AGNs. After a brief review of our current knowledge of emission from Blazars, I discuss some consequences of the recent detection made by {\it Chandra} of X-ray emission…
This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…
Passing from arithmetic schemes to algebraic schemes, in a similar manner we will have the computation of the \'etale fundamental group of an algebraic scheme and then will define and discuss the qc fundamental group of an algebraic scheme…
Systems of partial differential equations lie at the heart of physics. Despite this, the general theory of these systems has remained rather obscure in comparison to numerical approaches such as finite element models and various other…
We study jet schemes of Newton non-degenerate plane curve singularities. We identify a subgraph of the graph of jet components and show that it can be constructed from walks on the lattice points in the first quadrant of the Cartesian…
In this paper we state and prove some results on the structure of the jetbundles as left and right module over the structure sheaf on the projective line and projective space using elementary techniques involving diagonalization of…
In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.
In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…
Analysis of the Navier-Stokes equations in the frames of the algebraic approach to systems of partial differential equations (formal theory of differential equations) is presented.
This paper summarizes the results at the present moment about singularities with respect to the Mather-Jacobian log discrepancies over algebraically closed field of arbitrary characteristic. The basic point is the Inversion of Adjunction…
We discuss recent progress and open questions in QCD jet physics, with particular emphasis on two areas: jet definitions and jet substructure.
We review the following subjects: 1. Basic theory on algebraic curves and their moduli space, 2. Schottky uniformization theory of Riemann surfaces, and its extension called arithmetic uniformization theory, 3. Application to these theories…
The physics of astrophysical jets can be divided into three regimes: (i) engine and launch (ii) propagation and collimation, (iii) dissipation and particle acceleration. Since astrophysical jets comprise a huge range of scales and…
The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.
We introduce a new characteristic of jets called mass area. It is defined so as to measure the susceptibility of the jet's mass to contamination from soft background. The mass area is a close relative of the recently introduced catchment…
This article defines a new family of curves in space, whose graphs generate shapes similar to whirls. An intrinsic equation is found, in terms of curvature and torsion, which gives necessary and sufficient conditions for the existence of…
The geometry of jets of submanifolds is studied, with special interest in the relationship with the calculus of variations. A new intrinsic geometric formulation of the variational problem on jets of submanifolds is given. Working examples…
The global structure of the atmosphere and the oceans is a continuous source of intriguing challenges in geophysical fluid dynamics (GFD). Among these, jets are determinant in the air and water circulation around the Earth. In the last…
This is a note on the classical Waring's problem for several homogeneous forms. For positive integers (n,d,r,s), fix a general r-dimensional subspace of degree d forms in n+1 variables. We describe the family of s-sided polar polyhedra of…