General Mathematics
Partial ordinary Bell polynomials are used to formulate and prove a version of the Fa\`{a} di Bruno's formula which is convenient for handling nonlinear terms in the differential transformation. Applicability of the result is shown in two…
In this paper, the author introduces the concept of the symmetrized p-convex function, gives Hermite-Hadamard type inequalities for symmetrized p-convex functions.
We draw attention to a manuscript submitted to the HAL Open Archives by Francis Bessi\`ere, where he tries to base mathematics on a translative theory that could be shown consistant using only finitist methods, thus bypassing the…
Triangulation graph staining is sufficient for planar graph staining. This article will focus on triangulation and the nature of the color change channel of the staining tool. By construction, the four colors of the vertex are converted…
We derive an identity connecting any two second-order linear recurrence sequences having the same recurrence relation but whose initial terms may be different. Binomial and ordinary summation identities arising from the identity are…
The aim of the present paper is to study pseudo-symmetric, Ricci generalized pseudo-symmetric and generalized Ricci recurrent N(k)-Paracontact Metric Manifolds.
In this paper we have studied pseudosymmetric, Ricci-pseudosymmetric and projectively pseudosymmetric para-Sasakian manifold admitting a quarter-symmetric metric connection and constructed examples of 3-dimensional and 5-dimensional…
The last invited lecture published in $1962$ by Lanczos on his potential theory is never quoted because it is in french. Comparing it with a commutative diagram in a recently published paper on gravitational waves, we suddenly understood…
In this paper, by taking into account the beginning of the hypersurface theory in Euclidean space $E^4$, a practical method for the matrix of the Weingarten map (or the shape operator) of an oriented hypersurface $M^3$ in $E^4$ is obtained.…
In this paper we study the Theta splitting function $\Theta(s+1)$, a function defined on the positive integers. We study the distribution of this function for sufficiently large values of the integers. As an application we show that…
In this paper a randomized version of the Beverton-Holt type discrete model is proposed. Its solution stochastic process and the random steady state are determined. Its first probability density function and second probability density…
In this paper, new refinements for integral and sum forms of H\"older inequality are established. We note that many existing inequalities related to the H\"older inequality can be improved via obtained new inequalities in here, we show this…
This note generalizes the Fibonacci primitive roots to the set of integers. An asymptotic formula for counting the number of integers with such primitive root is introduced here.
What is a general expression for the sum of the first n integers, each raised to the mth power, where m is a positive integer? Answering this question will be the aim of the paper....We will take the unorthodox approach of presenting the…
In this paper we introduce the notion of bi-slant submanifolds of a para Hermitian manifold. They naturally englobe CR, semi-slant and hemi-slant submanifolds. We study their first properties and present a whole gallery of examples.
We derive a general recurrence relation for squares of Fibonacci-like numbers. Various properties are developed, including double binomial summation identites.
This paper explores special conditions on the starting value of a Collatz sequence which imply that the Collatz conjecture is true. This is the result of the collaboration of a retired mathematics professor (Koelzer) and a retired physics…
The pentagonal number theorem is extended to the sequence of the number of integer partitions with all parts equal. The new pentagonal number theorem implies that the distribution of the primes is just a specific detail of the application…
We create a simple test for distinguishing between sets of primes and random numbers using just the sum-of-digits function. We find that the sum-of-the-digits of prime numbers does not have an equal probability of being odd or even. The…
We propose a method to obtain iterative schemes guarantee unique solutions for systems of partial differential equations that are not symmetric with respect to the time by generalizing He variational iteration method and using Banach fixed…