- Détails du magazine
- Format
- Magazine
- eISSN
- 1844-0835
- Première publication
- 17 May 2013
- Période de publication
- 1 fois par an
- Langues
- Anglais

#### Chercher

- Accès libre

The extensibility of the Diophantine triple {2, b, c }

Pages: 5 - 24

#### Résumé

The aim of this paper is to consider the extensibility of the Diophantine triple {2,

#### Mots clés

- Diophantine tuples
- system of Pellian equations
- linear forms in logarithms

#### MSC 2010

- Primary 11D09
- Secondary 11D45, 11B37, 11J86

- Accès libre

Self dual, reversible and complementary duals constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4.

Pages: 25 - 50

#### Résumé

Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of

#### Mots clés

- Complementary dual codes
- Constacyclic codes
- Dual codes
- Frobenius rings
- Reversible codes
- Self-dual codes

#### MSC 2010

- Primary 94B15
- Secondary 94B05

- Accès libre

Notes on the zero-divisor graph and annihilating-ideal graph of a reduced ring

Pages: 51 - 70

#### Résumé

We translate some graph properties of 𝔸𝔾(_{t}_{t}

#### Mots clés

- Zero-divisor graph
- Annihilating-ideal graph
- Fixed-place ideal
- Ring of real-valued continuous
- Zariski-topology

#### MSC 2010

- 13A99
- 13A05
- 54C40

- Accès libre

Analysis of Control Interventions against Malaria in communities with Limited Resources

Pages: 71 - 91

#### Résumé

The aim of this paper is to analyse the potential impact of multiple current interventions in communities with limited resources in order to obtain optimal control strategies and provide a basis for future predictions of the most effective control measures against the spread of malaria. We developed a population-based model of malaria transmission dynamics to investigate the effectiveness of five different interventions. The model captured both the human and the mosquito compartments. The control interventions considered were: educational campaigns to mobilise people for diagnostic test and treatment and to sleep under bed nets; treatment through mass drug administration; indoor residual spraying(IRS) with insecticide to reduce malaria transmission; insecticide treated net (ITN) to reduce morbidity; and regular destruction of mosquito breeding sites to reduce the number of new mosquito and bites/contact at dusks and dawn. Analysis of the potential impact of the multiple control interventions were carried out and the optimal control strategies that minimized the number of infected human and mosquito and the cost of applying the various control interventions were determined.

#### Mots clés

- Optimal control
- Computational simulations
- Disease Free Equilibrium
- Pontryagin’s Maximum Principle
- stability theory

#### MSC 2010

- Primary 92B05; 92D25; 92D30
- Secondary 93D05; 34K20; 34K25

- Accès libre

A note on the ternary Diophantine equation x ^{2} − y ^{2}^{m} = z^{n}

^{2}−

^{2}

^{m}

^{n}

Pages: 93 - 105

#### Résumé

Let ℕ be the set of all positive integers. In this paper, using some known results on various types of Diophantine equations, we solve a couple of special cases of the ternary equation ^{2}^{2m}^{n}

#### Mots clés

- higher Diophantine equation
- exponential Diophantine equation
- generalized Fermat equation
- ternary equation

#### MSC 2010

- 11D41
- 1D61

- Accès libre

Fundamental solution matrix and Cauchy properties of quaternion combined impulsive matrix dynamic equation on time scales

Pages: 107 - 130

#### Résumé

In this paper, we establish some basic results for quaternion combined impulsive matrix dynamic equation on time scales for the first time. Quaternion matrix combined-exponential function is introduced and some basic properties are obtained. Based on this, the fundamental solution matrix and corresponding Cauchy matrix for a class of quaternion matrix dynamic equation with combined derivatives and bi-directional impulses are derived.

#### Mots clés

- Quaternion
- Cauchy matrix
- Combined matrix dynamic equation
- Bidirectional impulses
- Time scales

#### MSC 2010

- 34A37
- 34N05
- 11R52

- Accès libre

Two Points Taylor’s Type Representations for Analytic Complex Functions with Integral Remainders

Pages: 131 - 154

#### Résumé

In this paper we establish some two point weighted Taylor’s expansions for analytic functions

#### Mots clés

- Taylor’s formula
- Power series
- Logarithmic and exponential functions

#### MSC 2010

- Primary 30B10, 26D15
- Secondary 26D10

- Accès libre

A Benchmark Generalization of Fuzzy Soft Ideals in Ordered Semigroups

Pages: 155 - 171

#### Résumé

In real life, variability and inaccuracy are always presentand must be calculated by either possibilistic, probabilistic, polymorphic or other uncertainty approach. This benchmark study is about to construct new types of fuzzy soft ideals i.e., (∈, ∈ ∨_{k}_{k}_{λ}_{λ}_{λ}

#### Mots clés

- Fuzzy soft subsets
- OSGs (∈, ∈ ∨)-FSR(L)Is
- (∈∈ ∨)-fuzzy soft ideals
- level subsets

#### MSC 2010

- Primary 46G05, 46L05
- Secondary 47A30, 47B47

- Accès libre

On weakly S -prime ideals of commutative rings

Pages: 173 - 186

#### Résumé

Let

#### Mots clés

- -prime ideals
- Weakly -prime ideals
- -Noetherian rings
- Nagata idealization

#### MSC 2010

- Primary 13A15
- Secondary 13B02, 13E99

- Accès libre

Sums and products of intervals in ordered semigroups

Pages: 187 - 198

#### Résumé

We show a simple example for ordered semigroup 𝕊 = 𝕊 (+,⩽) that 𝕊 ⊆ℝ (ℝ denotes the real line) and ]

The multiplicative version of the above example is shown too.

The product of open intervals in the ordered ring of all integers (denoted by ℤ) is also investigated. Let _{x}_{+} and defined the function _{+} → ℤ_{+} by
_{+}. We give the function

Finally, we formulate some questions concerning the above topics.

#### Mots clés

- interval
- ordered dense Abelian group
- ordered field

#### MSC 2010

- Primary 39B22

- Accès libre

A Generalization of Archimedes’ Theorem on the Area of a Parabolic Segment

Pages: 199 - 209

#### Résumé

Archimedes’ well known theorem on the area of a parabolic segment says that this area is 4

#### Mots clés

- Archimedes’ theorem
- parabolic segment
- multiple integral
- spherical coordinates

#### MSC 2010

- 26B15
- 28A75
- 51M25

- Accès libre

Numerical solution of two-dimensional nonlinear fractional order reaction-advection-diffusion equation by using collocation method

Pages: 211 - 230

#### Résumé

In this article, two-dimensional nonlinear and multi-term time fractional diffusion equations are solved numerically by collocation method, which is used with the help of Lucas operational matrix. In the proposed method solutions of the problems are expressed in terms of Lucas polynomial as basis function. To determine the unknowns, the residual, initial and boundary conditions are collocated at the chosen points, which produce a system of nonlinear algebraic equations those have been solved numerically. The concerned method provides the highly accurate numerical solution. The accuracy of the approximate solution of the problem can be increased by expanding the terms of the polynomial. The accuracy and efficiency of the concerned method have been authenticated through the error analyses with some existing problems whose solutions are already known.

#### Mots clés

- Caputo fractional derivative
- Operational matrix
- Lucas polynomial
- Collocation method
- Reaction-advection-diffusion equation

- Accès libre

Strong convergence to a solution of the inclusion problem for a finite family of monotone operators in Hadamard spaces

Pages: 231 - 248

#### Résumé

In this paper, in the setting of Hadamard spaces, a iterative scheme is proposed for approximating a solution of the inclusion problem for a finite family of monotone operators which is a unique solution of a variational inequality. Some applications in convex minimization and fixed point theory are also presented to support the main result.

#### Mots clés

- Hadamard space
- Monotone operator
- Inclusion problem
- proximal point algorithm
- Variational inequality
- Strong convergence
- Convex minimization

#### MSC 2010

- Primary 47H05, 47H09
- Secondary 47J05, 65K05

#### Résumé

We give a stochastic order for Varma residual entropy and study several properties of it, like closure, reversed closure and preservation of this order in some stochastic models.

#### Mots clés

- Varma entropy
- Varma residual entropy
- Varma quantile entropy

#### MSC 2010

- 60E15
- 60K10
- 62E10
- 62N05
- 90B25

#### Résumé

In the paper, the concept of _{p}_{p}_{p}_{p}_{p}_{p}

#### Mots clés

- -radial addtion
- Dual quermassintegral
- Dual mixed quermassintegral
- Minkowski inequality
- Brunn-Minkowski inequality

#### MSC 2010

- Primary 52A40
- Secondary 46E30