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The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…
We prove a generalized Gauss-Kuzmin-L\'evy theorem for the $p$-numerated generalized Gauss transformation $$T_p(x)=\{\frac{p}{x}\}.$$ In addition, we give an estimate for the constant that appears in the theorem.
In this paper, we first propose a natural generalization of the well-known compare-and-swap object, one that replaces the equality comparison with an arbitrary comparator. We then present a simple wait-free universal construction using this…
We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.
Let $\mathfrak{g}$ be a basic simple Lie superalgebra over an algebraically closed field of characteristic zero, and $\theta$ an involution of $\mathfrak{g}$ preserving a nondegenerate invariant form. We prove that either $\theta$ or…
We appeal to a complex q-Fourier transform as a generalization of the (real) one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered ultra-distributions we are able to show that the q-Gaussian distribution can be…
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…
In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization,…
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…
A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case
We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary…
We consider Fujita's freeness conjecture in a relative setting and prove a criterion by proving a correct Q-divisor version of the Kollar vanishing theorem.
We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD thesis.
The goal of this article is to obtain a proof of the Main conjectures of Iwasawa theory for rational elliptic curves over anticyclotomic extensions of imaginary quadratic fields, under mild arithmetic assumptions, both in the case where the…
In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
The author in [7] was proved the generalized remainder and quotient theorems of polynomial in one indeterminate where the divisor is complete factorization to linear factors. In this paper we give the formula for the generalized remainder…
We propose generalized Fermat's conjecture in the framework of arithmetic dynamics, and give evidences. The multi-indexed version is added.
We construct the tensor product for f-algebras, including proving a universal property for it, and investigate how it preserves algebraic properties of the factors.
We give a purely combinatorial proof for the infinitary van der Waerden's theorem.