Related papers: The Ambiguous Class Number Formula Revisited

We formulate a conjecture which generalizes Darmon's "refined class number formula". We discuss relations between our conjecture and the equivariant leading term conjecture of Burns. As an application, we give another proof of the "except…

In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…

We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.

In previous work "Betweenness algebras" we introduced and examined the class of betweenness algebras. In the current paper we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras.…

In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.

We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.

This article present a new, direct and simple formula for constructing Mignotte sequences.

A probability method is provided to prove three classes of combinatorial identities. The method is extremely simple, only one step after the proper probability setup.

We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…

We find a formula for the number of solutions of linear congruence systems, by using elementary methods.

The regularized product of the Fibonacci numbers is evaluated.

In this article, using generalized derivations, we obtain a simple idea to prove the non-commutative Newton binomial formula in unital algebras and then, we extend that formula to non-unital algebras. Additionally, we establish the…

In the note, the author discovers an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.

We give a simple proof of the Fourier Inversion Theorem, using the methods of nonstandard analysis.

We prove some uniqueness results for weak solutions to some classes of parabolic Dirichlet problems.

In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.

We present a probabilistic proof of Euler's pentagonal number theorem based on a shuffling model.

We compute the index of a Lie Borel Lie Algbra of a simple Lie algebra.

An irreducible canonical approach to second-class constraints reducible of an arbitrary order is given. This method generalizes our previous results from [Europhys. Lett. 50 (2000) 169, J. Phys. A: Math. Theor. 40 (2007) 14537] for first-…

In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.