相关论文: The Fundamental Theorem of Barzilai does not hold

We show that the celebrated 1956 Lax-Richtmyer linear theorem in Numerical Analysis - often called the Fundamental Theorem of Numerical Analysis - is in fact wrong. Here "wrong" does not mean that its statement is false mathematically, but…

In this paper we follow a paper from A. Sedunova (2017) regarding R. C. Vaughan's basic mean value Theorem (Acta Arith. 1980) to improve and complete a more general demonstration for a suitable class of arithmetic functions as started by A.…

In this paper motivated by the celebrated fundamental theorem of algebra and its standard proof utilizing Liouville's Theorem, we prove the fundamental theorem of algebra type results for both commutative and noncommutative polynomials in…

The basic disentanglement theorem established by the present authors states that estimates on a weighted geometric mean over (convex) families of functions can be disentangled into quantitatively linked estimates on each family separately.…

Pairwise comparisons are used in a wide variety of decision situations where the importance of alternatives should be measured on a numerical scale. One popular method to derive the priorities is based on the right eigenvector of a…

We prove that the main theorem for absolutely monotonic functions from the book Mitrinovi\'{c}~D.S., Pe\v{c}ari\'{c}~J.E., Fink~A.M. "Classical And New Inequalities In Analysis", Kluwer Academic Publishers, 1993, is not valid without…

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

Set theory is widely believed to provide a secure foundation for deductive mathematics, but current set theories do not quite do this. The mainstream essentially uses na\"\i ve set theory. After Russell's paradox showed this to be…

This paper has been withdrawn by the author. The statement of the Main Theorem but is wrong in general, there have been provided counterexamples. The main theorem only holds conditionally, under the finiteness statement of theorem 2.8.

We generalise the Fundamental Theorem of Calculus to higher dimensions. Our generalisation is based on the observation that the antiderivative of a function of $n$-variables is a solution of a partial differential equation of order $n$…

There are several proofs of the Fundamental Theorem of Algebra, mainly using algebra, analysis and topology. In this article, we have shown that the Fundamental Theorem of Algebra can be proved using Nevanlinna's first fundamental theorem…

Proofs of the fundamental theorem of algebra can be divided up into three groups according to the techniques involved: proofs that rely on real or complex analysis, algebraic proofs, and topological proofs. Algebraic proofs make use of the…

The fundamental theorem of Riemannian geometry is inverted for analytic Christoffel symbols. The inversion formula, henceforth dubbed Ricardo's formula, is obtained without ancillary assumptions. Even though Ricardo's formula can…

Our interest is whether two binomial parameters differ, which parameter is larger, and by how much. This apparently simple problem was addressed by Fisher in the 1930's, and has been the subject of many review papers since then. Yet there…

A weight-dependent generalization of the binomial theorem for noncommuting variables is presented. This result extends the well-known binomial theorem for q-commuting variables by a generic weight function depending on two integers. For a…

In this paper, a detrimental mathematical mistake is pointed out in the proof of \textit{Theorem 1} presented in the paper\textit{ [Generalization of the gradient method with fractional order gradient direction, J. Franklin Inst., 357…

In this paper, we prove coincidence and common fixed points results under nonlinear contractions on a metric space equipped with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially…

Sellami and Sirvent conjectured that the balanced pair algorithm fails for the following pair of Pisot substitutions: \[ \varphi_0: \begin{array}{l} a \mapsto abc b \mapsto a c \mapsto ac \end{array} \quad \text{ and } \quad \varphi_1:…

In the Fermi Lectures on the obstacle problem in 1998, Caffarelli gave a proof of the mean value theorem which extends to general divergence form uniformly elliptic operators. In the general setting, the result shows that for any such…

For general mean-field backward stochastic differential equations (BSDEs) it is well-known that we usually do not have the comparison theorem if the coefficients depend on the law of $Z$-component of the solution process $(Y, Z)$. A natural…