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In this paper we study couples of finite separable extensions of the function field $\mathbb{F}_q(T)$ which are arithmetically equivalent, i.e. such that prime ideals of $\mathbb{F}_q[T]$ decompose with the same inertia degrees in the two…
Let $\alpha$ be an algebraic number of degree $d\ge 3$ having at most one real conjugate and let $K$ be the algebraic number field ${\mathbf Q}(\alpha)$. For any unit $\epsilon$ of $K$ such that ${\mathbf Q}(\alpha\epsilon)=K$, we consider…
We show that all smooth solutions of model non-linear sums of squares of vector fields are locally real analytic. A global result for more general operators is presented in a paper by Makhlouf Derridj and the first author under the title…
Recently, L. Guth improved the restriction estimate for the surfaces with strictly positive Gaussian curvature in R3. In this paper we generalize his restriction estimate to the surfaces with strictly negative Gaussian curvature.
We add some comments to our old paper \cite{F-U} where the metric tensor was introduced as the gauge theory of general coordinate transformation. This formulation is more satisfactorily completed than the original one if it is required to…
We prove two new reverse Cauchy--Schwarz inequalities of additive and multiplicative types in a space equipped with a positive sesquilinear form with values in a C*-algebra. We apply our results to get some norm and integral inequalities.…
Frobenius problem and its many generalizations have been extensively studied in several areas of mathematics. We study semigroups of totally positive algebraic integers in totally real number fields, defining analogues of the Frobenius…
We present a general refinement of the Cauchy-Schwarz inequality over complete inner product spaces and show that it can be of interest for some statistical applications. This generalizes and simplifies previous results on the same subject.
In this paper, new refinements for integral and sum forms of H\"older inequality are established. We note that many existing inequalities related to the H\"older inequality can be improved via obtained new inequalities in here, we show this…
We provide analytical solutions to the thermodynamic Bethe ansatz equations in the large and small density approximations. We extend results previously obtained for leading order behaviour of the scaling function of affine Toda field…
This is the first of a series of papers studying real algebraic threefolds using the minimal model program. The main results are outlined in Part II. The present part I. contains the necessary preliminary work concerning terminal…
We obtain rates of convergence of numerical approximations of abstract linear parabolic evolution equations in Banach spaces. Our estimates extend known results from the literature of finite element approximations of parabolic equations to…
In this paper, we give a new inequality for convex functions of real variables, and we apply this inequality to obtain considerable generalizations, refinements, and reverses of the Young and Heinz inequalities for positive scalars.…
We prove inequalities involving intrinsic and extrinsic radii and diameters of tetrahedra.
Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces that improve some earlier results are pointed out. They are applied to obtain new Gruss type inequalities in inner product spaces. Some natural applications for…
Problems of absolute G measurements, its temporal and range variations from both experimental and theoretical points of view are discussed, and a new universal space project for measuring G, G(r) and G-dot promising an improvement of our…
We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conjecture, as proved for curves and abelian varieties by…
In this paper, we generalize the arithmetic functions $\tau$ and $\tau^{\left(e\right)}$ in algebraic number fields and we find some properties of these functions.
The purpose of this paper is to generalize some results of Gross-Zagier [20] and Kolvyvagin [28] to totally real fields.
We introduce a notion of refinements in the context of patching, in order to obtain new results about local-global principles and field invariants in the context of quadratic forms and central simple algebras. The fields we consider are…