Issam Kaddoura

Lebanese International University | LIU · Department of Mathematics

In this article, we establish a new closed formula for the solution of homogeneous second-order linear difference equations with constant coefficients by using matrix theory. This, in turn, gives new closed formulas concerning all sequences of this type such as the Fibonacci and Lucas sequences. Next, we show the main advantage of our formula which...

In this paper, we study a particular class of block matrices placing an emphasis on their spectral properties. Some related applications are then presented. In particular, we prove the existence of an infinite number of integer matrix solutions for the two equations: aX p + bY p = cZ p and aX p + bY q = cZ r for any integers a, b and c and for any...

This article examines the necessary conditions for the unique existence of solutions to nonlinear implicit ϑ -Caputo fractional differential equations accompanied by fractional order integral boundary conditions. The analysis draws upon Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Furthermore, the circumstances leading to...

Here, we investigate the existence of solutions for the initial value problem of fractional-order differential inclusion containing nonlocal infinite-point or Riemann-Stieltjes integral boundary conditions. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the solution will be studied. Finally,...

Here, we investigate the existence of solutions for the initial value problem of fractional-order differential inclusion containing a non-local infinite-point or Riemann-Stieltjes integral boundary conditions. A sufficient condition for the uniqueness of the solution is given. The continuous dependence of the solution on the set of selections and o...

In this paper, the existence and Ulam-Hyers stability of solutions for implicit second order fractional differential equations are investigated via fractional-orders integral boundary conditions. Our results are based on Krasnoselskii's fixed point Theorem and Banach contraction principle. We provide examples at the end to clarify our acquired outc...

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 this paper, we study a particular class of block matrices placing an emphasis on their spectral properties. Some related applications are then presented.

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.