Research Papers/Topics in Mathematics

The Implicit Midpoint Rule of Non-expansive Mappings and Applications in Uniformly Smooth Banach Space

Let K be a nonempty closed convex subset of a Banach space E and T : K → K be a nonexpansive mapping. Using a viscosity approximation method, we study the implicit midpoint rule of a nonexpansive mapping T. We establish a strong convergence theorem for an iterative algorithm in the framework of uniformly smooth Banach spaces and apply our result to obtain the solutions of an accretive mapping and a variational inequality problem. The numerical example which compares the rates of convergence...

Espil's high power partial fraction decomposition theorem.

The problem of fraction decomposition it's easy to solve by using the cover up method, when there are no repeated linear factors in the denominator . Nevertheless it could turn into a hard work if these factors are raised to a high power, where the cover up method doesn't work. This technique shows how to calculate these coefficients without solving large systems of equations with a clever rearrangement of the numerator.

Espil's theorem corollary

shortly from the Espil's theorem, we can derive the generalized Dirichlet integral for any natural value when the hole integrand is raised to the n-th power.

Integration technique using Laplace Transforms. A generalized form of the Dirichlet integral.

The problem of integration technique over integrands of the form f(t)/t^n, can be solved by differentiation(n times)  by using Leibniz's rule to get rid of t^n, that leads to integrate back (n times) to end the game which it's harder than the original problem.This work focuses on the derivation of the formula (Espil's Theorem) which is a perfect tool to avoid that hard task. It allows to change the difficult n iterated integrals  into a more outstanding easier problem which consists of n-1 ...

It is Time to Move Research Expenditures to the Denominator in University Metrics

An unintended consequence of using “research expenditures” as a figure of merit for universities is to reduce the research output per dollar invested by discouraging the diffusion of superior, lower-cost, open-source scientific equipment.


Trigonometry (from Greek trigōnon, "triangle" and metron, "measure"[1]) is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.[2]The 3rd-century astronomers first noted that the lengths of the sides of a right-angle triangle and the angles between those sides have fixed relationships: that is, if at least the...


Contents1 General Introduction 11.1 Background of Study . . . . . . . . . .11.2 Integral Equation . . . . . . . . . .......21.2.1 Fredholm integral equation . . .31.2.2 Volterra integral equation . . . . 41.3 Polynomials . . . . . . . . . . . . . . . . . 41.4 Orthogonal Polynomials . . . . . . .51.5 Chebyshev Polynomials . . . . . . . 61.5.1 Chebyshev polynomial of the first kind Tr(x) . . . . . 61.5.2 Chebyshev polynomial of second kind Ur(x) . . . . . 61.5.3 Chebyshev polynomials of third-k...

Systematic study of z transform and its analysis on Discrete Time Systems

                    ABSTRACTIn this project work, we have established a systematic study of z transform and its analysis on Discrete Time (DT) systems. The researcher also deal with Linear Time Invariant (LTI) system and Difference Equation as examples of DT systems. The right and left shift was use as a method of solution of the z transform to linear difference equation.CHAPTER 1          &nb...

The relationships between students’ attitude towards mathematics and their performance in mathematics

It is said that mathematics is the gate and key of the sciences. According to the famous philosopher Kant, “A science is exact only in so far as it employs mathematics”. So all scientific education which does not commence with mathematics is said to be defective at its foundation, In fact it has formed the basis for the evolution of scientific development all over. Taking into cognizance, the usefulness, relevance and importance of mathematics, like bringing positive changes to the scient...


Research Thesis on Formulation of HAMILTONIAN MECHANICS reconciliation of Classical Mechanics (Langrangian) with Quantum Mechanics (Hamiltonian), smaller infinitesimal particles Einstein's Mechanics.Addendum, Canonical Transformation, Principle of Virtual Work, Harmonic Oscillator and Lemma on Mathematical Method ascertained by PROF. J.C AMAZIGO DEPARTMENT OF MATHEMATICS UNIVERSITY OF NIGERIA NSUKKA.

The Effect of Anxiety on Performance of Students in Mathematics: A Case Study of Adeniran Ogunsanya College of Education, Lagos State, Nigeria

This research work ‘’THE EFFECT OF ANXIETY ON PERFORMANCE OF STUDENTS IN MATHEMATICS’’ focuses on the relationship between Mathematics anxiety and students performance. A descriptive experimental research design was used to investigate the research questions. The population consisted of 120 pre-service teachers at Adeniran Ogunsanya College of Education, Ojo Local Government, Lagos State. A personal data questionnaire was used to gather demographic and anxiety information about the pa...


1 Riemann Integration 21.1 Partitions and Riemann sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.1 Definition  (Partition P of size  > 0) . . . . . . . . . . . . . . . . . . . . 21.1.2 Definition (Selection of evaluations points zi) . . . . . . . . . . . . . . . . 21.1.3 De finition (Riemann sum for the function f(x)) . . . . . . . . . . . . . . 21.1.4 Defi nition (Integrability of the function f(x)) . . . . . . . . . . . . . . . 21.1.5 De finition (Notation for integrab...

Arithmetic of Analysis (Supremum and Infimum)

I can still remember my expression and feeling when we were asked to show that sup(A + B) = sup(A) + sup(B). It was an herculean task because the concept was too difficult to grasp with the use of approximation property until I discovered an easy route. In a bid to restrict my papers to just few pages, I will focus more on examples than theorems.

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