Related papers: A Direct Proof of Landen's Transformation
We develop a notion of linear strands for multigraded free resolutions, and we prove a multigraded generalization of Green's Linear Syzygy Theorem.
We derive the general formula for Lorentz-transformed spin density matrix. It is shown that an appropriate Lorentz transformation can prduce totally unpolarized state out of pure one. Further properties, as depurification by an arbitrary…
We deal with very weak positive supersolutions to the H\'enon-Lane-Emden system on neighborhoods of the origin. In our main theorem we prove a sharp nonexistence result.
We give an exact coefficients formula of any infinite product of power series with constant term equal to $1$, by using structures from partitions of integers and permutation groups. This is an universal theorem for various of Binomial-type…
We prove a transformation formula relating two determinants involving elliptic shifted factorials. Similar determinants have been applied to multiple elliptic hypergeometric series.
We formulate and prove finite dimensional analogs for the classical Balian-Low theorem, and for a quantitative Balian-Low type theorem that, in the case of the real line, we obtained in a previous work. Moreover, we show that these results…
We provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural definitions for generalized Bernoulli numbers and polynomials of…
In this paper, we present a simple analytic proof of Siegel's theorem that concerns the lower bound of $L(1,\chi)$ for primitive quadratic $\chi$. Our new method compares an elementary lower bound with an analytic upper bound obtained by…
An effective hamiltonian is derived exactly for the one-dimensional periodic Anderson model via a canonical transformation. The canonical transformation has been calculated up to infinite order, thus an exact transformation was performed in…
Elementary methods are used to examine some nontrivial mathematical issues underpinning the Lorentz transformation. Its eigen-system is characterized through the exponential of a $G$-skew symmetric matrix, underlining its unconnectedness at…
Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…
In this note, we prove that there exist infinite dimensional excellent rings.
We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.
The main purpose of the paper is to demonstrate that condition of invariance with respect to the Legendre transformations allows effectively isolate the class of integrable difference equations on the triangular lattice, which can be…
We present new classes of permutation polynomials over finite fields.
Assuming the Generalized Riemann Hypothesis we obtain uniform, effective number-field analogues of Mertens' theorems.
We use elementary triangular matrices to obtain some factorization, multiplication, and inversion properties of triangular matrices. We also obtain explicit expressions for the inverses of strict $k$-Hessenberg matrices and banded matrices.…
The Lorentz Transformation is derived from only three simple postulates: (i) a weak kinematical form of the Special Relativity Principle that requires the equivalence of reciprocal space-time measurements by two different inertial…
We prove some formulas relating the inverse of a Cartan matrix with algebraic and geometric invariants of finite group representations.
We derive explicit formulas for the inverses of the Cartan matrices of the simple Lie algebras and the basic classical Lie superalgebras, as well as for their infinite generalizations.