相关论文: Some divergent trigonometric integrals

A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…

This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…

In the present paper, we have developed a method for solving \textit{diophantine inequalities} using their relationship with the \textit{difference between consecutive primes}. Using this approach we have been able to prove some theorems,…

Discretization of curves is an ancient topic. Even discretization of curves with an eye toward differential geometry is over a century old. However there is no general theory or methodology in the literature, despite the ubiquitous use of…

We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this form over a totally real extension of odd degree. We prove…

In this paper, a theorem about similar triangles is proved. It shows that two small and four large triangles similar to the original triangle can appear if we choose well among several intersections of the perpendicular bisectors of the…

In this paper we consider the iteration of infinitely many signed exponentials with the same base but the signs may vary. We show that for every base in an explicit interval this iteration converges for any sequence of signs and all the…

We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…

We prove that any derived equivalence between derived discrete algebras is standard, i.e.\ is isomorphic to the derived tensor product by a two-sided tilting complex.

Mixed trigonometric-polynomials frequently occur in applications in physics, numerical analysis and engineering, the algorithm has been already proposed to determine its sign on (0,{pi}/2]. This paper proposes a procedure to extend the…

This paper has been withdrawn by the author, due to a crucial error in the proof of Thm.1

Few among us would know that the first mention of the sine and the enumeration of the first sine table are to be credited to Aryabhata. The method to generate this relies on the sine difference formula which is derived using ingenious…

It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples…

We describe various errors in the mathematical literature, and consider how some of them might have been avoided, or at least detected at an earlier stage, using tools such as Maple or Sage. Our examples are drawn from three broad…

We show that the ``effective Lagrangian'' constructed in [1] is inconsistent with the exact result for the complete Lagrangian presented in [2]. We trace the origin of the inconsistence to the peculiar way in which the path integral methods…

This paper offers what seems at first to be a minor technical correction to the current practice of computing indefinite integrals, and introduces the idea of a "Kahanian constant of integration". However, the total impact of this minor…

This paper considers some integrals where the integrand comprises the log gamma function or the digamma function multiplied by exponential or trigonometric functions.

We introduce the notion of a graph derangement, which naturally interpolates between perfect matchings and Hamiltonian cycles. We give a necessary and sufficient condition for the existence of graph derangements on a locally finite graph.…

The diagram showing off-center nested spheres which is traditionally used to illustrate the Doppler effect, is misleading and its trigonometric analysis leads to errors concerning light, because electromagnetic Doppler and aberration…

A possible method to solve the sign problem is developed by modifying the original theory. Considering several modifications of the partition function, the observable in the original theory is reconstructed from the identity connecting the…