# Issam KaddouraLebanese International University | LIU · Department of Mathematics

Issam Kaddoura

Ph.D

## About

36

Publications

99,970

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99

Citations

Introduction

Additional affiliations

September 2016 - present

Education

October 1996 - October 2000

## Publications

Publications (36)

In the paper, motivated by the generating function of the Catalan numbers in combinatorial number theory and with the aid of Cauchy’s integral formula in complex analysis, the authors generalize the Catalan numbers and its generating function, establish an explicit formula and an integral representation for the generalization of the Catalan numbers...

In the paper, employing methods and techniques in analysis and linear algebra, the authors find a simple formula for computing an interesting Hessenberg determinant whose elements are products of binomial coefficients and falling factorials, derive explicit formulas for computing some special Hessenberg and tridiagonal determinants, and alternative...

In the paper, motivated by the generating function of the Catalan numbers in combinatorial number theory and with the aid of Cauchy's integral formula in complex analysis, the authors generalize the Catalan numbers and its generating function, establish an explicit formula and an integral representation for these generalizations of the Catalan numb...

In the paper, employing methods and techniques in analysis and linear algebra, the authors find a simple formula for computing an interesting Hessenberg determinant whose elements are products of binomial coefficients and falling factorials, derive explicit formulas for computing some special Hessenberg and tridiagonal determinants, and alternative...

The aim of this study is to observe and assess the performance of Psychrotrophic Gram-negative bacteria, namely Pseudomonas fluorescens, which pose a significant spoilage problem in food, under different temperature, water activity (aw) and pH conditions. Noting that at aw 0.6 and 0.75 irrespective of temperature or pH and at temperatures 60 0 and...

In this paper, we determine a sufficient condition for the asymptotic stability of the
equilibrium point of the autonomous dynamical system.

In this paper, we study the interesting combinatorial numbers of Delannoy and construct a new closed formula in a matrix form.

Abstract: In this paper, we study the amazing geometrical properties of the Fibonacci sequence, and we prove that the consecutive values of the Fibonacci ordered pairs (F_n, F_n+1) belong to a double hyperbola where the tangent T (F_n, F_n+1), the normal N(F_n, F_n+1), and the binormal B(F_n, F_n+1) vectors inherit the same behavior of Fibonacci re...

In this paper, we use some extension of the Cayley-Hamilton theorem to find a family of matrices with integer entries that satisfy the non-linear Diophantine equation $ x^{n}+y^{p}=z^{q}$ where $n,p$ and $q$ are arbitrary positive integers.

In this paper, we study a particular class of matrices generated by generalized permutation matrices corresponding to a subgroup of some permutation group. As applications, we first present a technique from which we can get closed formulas for the roots of many families of polynomial equations with degree between 5 and 10, inclusive. Then, we descr...

In this paper, we construct a new family of elliptic curves E (m, N, M) (Fp) over the field Fp where p is a prime number. And we count the cardinality #E (m, N, M) (Fp).

In this paper, we expand and approximate analytic complex function f(z) as a continued fraction and a matrix multiplication Form.

In this paper, we establish a new general framework under which all generalized Fibonacci-type sequences come together. The main result lies in obtaining one new general closed formula solution for all such sequences by using only matrix theory. This new formula in turn gives new closed formula solutions for most well-known sequences of this type....

In this paper, we establish a new closed formula for the solution of homogeneous second order linear difference equations with constant coefficients by using only matrix theory. This, in turn, gives new closed formulas for many sequences of this type such as Fibonacci and Lucas sequences and many others. Then we present two applications: one deals...

In this paper, we present a new family of matrices which can be used to determine
the roots of the cubic and quartic polynomials. Using the same approach, we determine a
system of non-linear equations whose solution provides complete solutions of some quintic
polynomials.

In this paper, we use some extension of the Cayley-Hamilton theorem
to find a family of matrices with integer entries that satisfy the non-linear Diophantine equation
x^n +y^p = z^q where n, p, and q are arbitrary positive integers.

In this paper, we use the algebra of matrix theory to construct new formulas for the nth Lucas and Fibonacci numbers. The new formulas involve matrices with integer entries. They are simple, eﬃcient, and provide a new approach for ﬁnding many new identities, relations, and theorems.

In this paper, we give a new semi primality test and we construct a new formula for $\pi ^{(2)}(N)$, the function that counts the number of semiprimes not exceeding a given number $N$. We also present new formulas to identify the $n^{th}$ semiprime and the next semiprime to a given number. The new formulas are based on the knowledge of the primes l...

In this paper, we give a new semi primality test, and we construct a new formula to count the number of semiprimes not exceeding a given number N. We also present new formulas to identify the n^th semiprime and the next semiprime to a given number.

In this paper, we prove some identities including Lucas numbers and primes.

In this paper we construct an analog to pascal's triangle that characterize
primes with additional fascinating properties .

We prove that for all positive integers n, p and q the equations xn + yn = zn
as well as an + bp = cq have infinite number of non -trivial solutions over the
square matrices with integer entries. At the end, we present theorems that are
analog to that of Fermat and Euler in matrix form.

In this conference paper, we construct analog to Pascal's triangle that
characterize primes with additional fascinating properties.

There are many different types of Lyapunov theorems, but the key in all cases is to find a Lyapunov function and verify that it has the required properties. A well- known approach is to guess a parametrized Lyapunov function candidate then try to find the values of the parameters so that the required conditions hold. In this paper, we can construct...

William Browder in his paper "Surgery and the theory of differentiable
transformation groups" developed surgery techniques to study semi-free actions
of S1 on homotopy spheres, under the additional assumption that the fixed point
set is a homotopy sphere. He used this surgery to show how to construct such
actions. In this paper, I discussed a simil...

In this note, we present an algorithm that yields a new method for constructing doubly stochastic and symmetric doubly stochastic matrices for the inverse eigenvalue problem. In addition, we introduce new open problems in this area that lay the ground for future work.

What we intend to do in this paper is to ease the primality test of very large numbers so that primality is conﬁrmed with high probability within a short time.

In the paper of Montgomery, D. and Yang, C.T. [5], they discuss the
de-suspension of smooth free actions of S1 on (2n+1)-dimensional homotopy
spheres. In this paper we discuss the de-suspension of smooth free actions of
S3 on (4n + 3)-dimensional homotopy spheres.

In this paper, we propose a new primality test, and then we employ this test
to find a formula for {\pi} that computes the number of primes within any
interval. We finally propose a new formula that computes the nth prime number
as well as the next prime for any given number

In this note, we prove that the conjecture giving in [14] concerning the inverse eigenvalue problem for 4 × 4 symmetric doubly stochastic matrices, is wrong. In addition, a new subset of the region where the decreasingly ordered spectra of 4 × 4 symmetric doubly stochastic lie, is found, and an alternative conjecture concerning the same problem is...

In this note, we give a generalization of some extension of the Cayley-Hamilton theorem in the case of a pair of n × n commuting matrices to the case of a pair of n×n non-commuting matrices. The classical Cayley-Hamilton theorem and its extension in the case of pairs of commuting matrices, are special cases of the proposed generalization.

We obtain a new formula that gives the complete solutions of the Linear Diaphontine Equation
in terms of arbitrary parameters.

## Questions

Questions (18)

## Projects

Projects (8)

Our goal is to find a unified closed formula that counts all Delannoy- type numbers. For this purpose, we consider all the paths that traverse from one vertex to the other vertices according to the desired Delannoy type strategies. And construct the required formula with (0,1) matrix entries.

For a given matrix A ∈M_{n}(F), F=R or C.
The spectrum ρ(A) is bounded by a region Ω(A)⊂C determined by the constraints over ρ(A) which are guaranteed by a special technique
We embed the matrix A_{nn} with random variables x ∈F^{k} such that
a new variable matrix B(x) is obtained with the condition
ρ(A)⊆ ρ(B(x)) ⊂ Ω(B(x)) ⊂ C
and consequently the new region Ω(B(x)) varies with x ∈F^{k}.
Our goal is to find min_{x∈F} Ω(B(x))=Ω^{∗} ⊆ Ω(A).
This will improve the bounds of the eigenvalues.
(2) To study the stability of the equilibrium states of some dynamical system and to show that asymptotic stability of the dynamical system is equivalent to find min_{x∈F} Ω(B(x))=Ω^{∗}⊆Ω(J)⊆{z∈C, Rez<0}.

In this project, we are working on studying the amazing geometrical properties of the Fibonacci - type sequences. We consider the double Fibonacci - level hyperbolic curves and investigate the potential geometric properties that may inherit from the golden asymptotic behavior of the sequence average.