More on the sum-freedom of the multiplicative inverse function

Crossed S-matrices and character sheaves on unipotent groups

Interpreting Correlated Motions Using Normal Mode Analysis

Let X be a complete non-singular algebraic curve over an algebraically closed field k of positive characteristic p. Let F: Ox―>Qx be the Frobenius homomorphism F(a)=ap, and denote the induced /^-linearmap H\X, Ox)-* H\X, Ox) again by F, which is called the Hasse-Witt map. The dimension of the semi-simple subspace H\X, Ox)s of H\X, Ox) is denoted by a(X) and called the £-rank of a curve X, which is equal to the jb-rank of the Jacobian variety of X. Let 7t:X-*Y be a /^-cyclicovering of complete non-singular curves over k. Then the Deuring-Safarevic formula is the following:

Symmetric subgroup invariants in irreducible representations of GF, when G=GLn

It has been established that certain trilinear froms of three perspective views give rise to a tensor of 27 intrinsic coefficients [8]. Further investigations have shown the existence of quadlinear forms across four views with the negative result that further views would not add any new constraints [3, 12, 5]. We show in this paper first general results on any number of views. Rather than seeking new constraints (which we know now is not possible) we seek connections across trilinear tensors of triplets of views. Two main results are shown: (i) trilinear tensors across m>3 views are embedded in a low dimensional linear subspace, (ii) given two views, all the induced homography matrices are embedded in a four-dimensional linear subspace. The two results, separately and combined, offer new possibilities of handling the consistency across multiple views in a linear manner (via factorization), some of which are further detailed in this paper.

Let and let and be two convex bodies in such that their orthogonal projections and onto any ‐dimensional subspace are directly congruent, that is, there exists a rotation and a vector such that . Assume also that the 2‐dimensional projections of and are pairwise different and they do not have ‐symmetries. Then and are congruent. We also prove an analogous more general result about twice differentiable functions on the unit sphere in .

This chapter is devoted to developing ergodic theorems first for relative entropy densities and then information densities for the general case of AMS processes with standard alphabets. The general results were first developed by Barron using the martingale convergence theorem and a new martingale inequality. The similar results of Algoet and Cover can be proved without direct recourse to martingale theory. They infer the result for the stationary Markov approximation and for the infinite order approximation from the ordinary ergodic theorem. They then demonstrate that the growth rate of the true density is asymptotically sandwiched between that for the kth order Markov approximation and the infinite order approximation and that no gap is left between these asymptotic upper and lower bounds in the limit as k → ∞. They use martingale theory to show that the values between which the limiting density is sandwiched are arbitrarily close to each other, but in this chapter it is shown that martingale theory is not needed and this property follows from the results of Chapter 8.

On connected line sets of antiflag class [formula omitted] in [formula omitted

Constitutive structure of rate theory of damage in brittle elastic solids

Relative bases in Banach spaces

The effect of finite rank perturbations on Jordan chains of linear operators

A chain of quadratic first integrals of general linear Hamiltonian systems that have not been represented in canonical form is found. Their involutiveness is established and the problem of their functional independence is studied. The key role in the study of a Hamiltonian system is played by an integral cone which is obtained by setting known quadratic first integrals equal to zero. A singular invariant isotropic subspace is shown to pass through each point of the integral cone, and its dimension is found. The maximal dimension of such subspaces estimates from above the degree of instability of the Hamiltonian system. The stability of typical Hamiltonian systems is shown to be equivalent to the degeneracy of the cone to an equilibrium point. General results are applied to the investigation of linear mechanical systems with gyroscopic forces and finite-dimensional quantum systems.

All-Time Existence of Smooth Solutions to PDEs of Mixed Type and the Invariant Subspace of Uniform States

In this study, rather than transitioning directly from geometric structures to graph theory, we have derived several general results and theorems concerning the coloring of points and lines within affine and projective structures. We approached this topic through the lens of vertex and edge coloring concepts, pivotal subjects within graph theory. Our investigation sheds light on the intricate relationship between geometric structures and graph theory, providing a novel perspective on coloring methodologies. Extending the principles of vertex and edge coloring to affine and projective spaces, we uncover fundamental insights into the interplay between geometry and combinatorial mathematics.

We developed an inverse technique based on the Boltzmann-Matano method from which apparent coefficients of diffusion of decaying radionuclides in saturated porous media can be calculated. The technique uses the assumption that the concentration profiles (or breakthrough curves) have S shapes and can be well approximated by the error function with three adjustable parameters (the position, height, and slope). The resulting dependence of the apparent diffusion coefficient on concentration was given as a rather simple formula involving inverse error function. Here we wish to apply this straightforward technique to obtain concentration dependences of the apparent diffusion coefficients of 22Na+ and 134Cs+ for which the corresponding breakthrough curves were measured for two types of dense opalinus clay rocks. We compare our more general results with those from the original study in which the apparent diffusion coefficient was assumed to be constant and indicate that the latter approach need not be appropriate.