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Volume 30 (2022): Edition 2 (May 2022)

Volume 30 (2022): Edition 1 (February 2022)

Volume 29 (2021): Edition 3 (November 2021)

Volume 29 (2021): Edition 2 (June 2021)

Volume 29 (2021): Edition 1 (March 2021)

Volume 28 (2020): Edition 3 (December 2020)

Volume 28 (2020): Edition 2 (July 2020)

Volume 28 (2020): Edition 1 (March 2020)

Volume 27 (2019): Edition 3 (December 2019)

Volume 27 (2019): Edition 2 (June 2019)

Volume 27 (2019): Edition 1 (March 2019)

Volume 26 (2018): Edition 3 (December 2018)

Volume 26 (2018): Edition 2 (July 2018)

Volume 26 (2018): Edition 1 (March 2018)

Volume 25 (2017): Edition 3 (December 2017)

Volume 25 (2017): Edition 2 (July 2017)

Volume 25 (2017): Edition 1 (January 2017)

Volume 24 (2016): Edition 3 (November 2016)

Volume 24 (2016): Edition 2 (June 2016)

Volume 24 (2016): Edition 1 (January 2016)

Volume 23 (2015): Edition 3 (November 2015)

Volume 23 (2015): Edition 2 (June 2015)

Volume 23 (2015): Edition 1 (January 2015)

Volume 22 (2014): Edition 3 (September 2014)

Volume 22 (2014): Edition 2 (June 2014)

Volume 22 (2014): Edition 1 (March 2014)

Volume 21 (2013): Edition 3 (November 2013)

Volume 21 (2013): Edition 2 (June 2013)

Volume 21 (2013): Edition 1 (March 2013)

Volume 20 (2012): Edition 3 (December 2012)

Volume 20 (2012): Edition 2 (June 2012)
Proceedings of the 10th International Workshop on Differential Geometry and its Applications

Volume 20 (2012): Edition 1 (May 2012)

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

Chercher

Volume 29 (2021): Edition 2 (June 2021)

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

Chercher

15 Articles
Accès libre

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

Publié en ligne: 08 Jul 2021
Pages: 5 - 24

Résumé

Abstract

The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of c’s (depending on b). As corollary, for example, we prove that for b/2 − 1 prime, all Diophantine quadruples {2, b, c, d} with 2 < b < c < d are regular.

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.

Publié en ligne: 08 Jul 2021
Pages: 25 - 50

Résumé

Abstract

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 γ-constacyclic codes is established and the algebraic characterization of self-dual, reversible γ-constacyclic codes and γ-constacyclic codes with complementary dual are given.

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

Publié en ligne: 08 Jul 2021
Pages: 51 - 70

Résumé

Abstract

We translate some graph properties of 𝔸𝔾(R) and Γ(R) to some topological properties of Zariski topology. We prove that the facts “(1) The zero ideal of R is an anti fixed-place ideal. (2) Min(R) does not have any isolated point. (3) Rad(𝔸𝔾 (R)) = 3. (4) Rad(Γ(R)) = 3. (5) Γ(R) is triangulated (6) 𝔸𝔾 (R) is triangulated.” are equivalent. Also, we show that if the zero ideal of a ring R is a fixed-place ideal, then dtt(𝔸𝔾 (R)) = |ℬ(R)| and also if in addition |Min(R)| > 2, then dt(𝔸𝔾 (R)) = |ℬ (R)|. Finally, it is shown that dt(𝔸𝔾 (R)) is finite if and only if dtt(𝔸𝔾 (R)) is finite if and only if Min(R) is finite.

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

Publié en ligne: 08 Jul 2021
Pages: 71 - 91

Résumé

Abstract

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 x2y2m = zn

Publié en ligne: 08 Jul 2021
Pages: 93 - 105

Résumé

Abstract

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 x2y2m = zn, x, y, z, m, n ∈ ℕ, gcd(x, y) = 1, m ≥ 2, n ≥ 3.

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

Publié en ligne: 08 Jul 2021
Pages: 107 - 130

Résumé

Abstract

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

Publié en ligne: 08 Jul 2021
Pages: 131 - 154

Résumé

Abstract

In this paper we establish some two point weighted Taylor’s expansions for analytic functions f : D ⊆ ℂ→ ℂ defined on a convex domain D. Some error bounds for these expansions are also provided. Examples for the complex logarithm and the complex exponential are also given.

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

Publié en ligne: 08 Jul 2021
Pages: 155 - 171

Résumé

Abstract

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., (∈, ∈ ∨qk)-FSR(L)Is of ordered semigroup(OSG). Based on this inception, fuzzy soft level subsets are defined which link ordinary ideals with (∈, ∈ ∨qk)-fuzzy soft left(right) ideals. Some binary operations like ◦λ, intersection ∩λ and union of fuzzy soft sets ∪λ are given and various fundamental results of ideal theory are developed through these types of fuzzy soft ideals.

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

Publié en ligne: 08 Jul 2021
Pages: 173 - 186

Résumé

Abstract

Let R be a commutative ring with identity and S be a multiplicative subset of R. In this paper, we introduce the concept of weakly S-prime ideals which is a generalization of weakly prime ideals. Let P be an ideal of R disjoint with S. We say that P is a weakly S-prime ideal of R if there exists an sS such that, for all a, bR, if 0 ≠ abP, then saP or sbP. We show that weakly S-prime ideals have many analog properties to these of weakly prime ideals. We also use this new class of ideals to characterize S-Noetherian rings and S-principal ideal rings.

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

Publié en ligne: 08 Jul 2021
Pages: 187 - 198

Résumé

Abstract

We show a simple example for ordered semigroup 𝕊 = 𝕊 (+,⩽) that 𝕊 ⊆ℝ (ℝ denotes the real line) and ]a, b[ + ]c, d[ = ]a + c, b + d[ for all a, b, c, d ∈ 𝕊 such that a < b and c < d, but the intervals are no translation invariant, that is, the equation c +]a, b[ = ]c + a, c + b[ is not always fulfilled for all elements a, b, c ∈ 𝕊 such that a < b.

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 Ix := {1, 2, . . ., x} for all x ∈ ℤ+ and defined the function g : ℤ+ → ℤ+ by g(x):=max{ y+|IyIxIx } g\left( x \right): = \max \left\{ {y \in {\mathbb{Z}_ + }|{I_y} \subseteq {I_x} \cdot {I_x}} \right\} for all x ∈ ℤ+. We give the function g implicitly using the famous Theorem of Chebishev.

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

Publié en ligne: 08 Jul 2021
Pages: 199 - 209

Résumé

Abstract

Archimedes’ well known theorem on the area of a parabolic segment says that this area is 4/3 of the area of a certain inscribed triangle. In this paper we generalize this theorem to the n-dimensional euclidean space, n ≥ 3. It appears that the ratio of the volume of an n-dimensional solid bounded by an (n − 1)-dimensional hyper-paraboloid and an (n − 1)-dimensional hyperplane and the volume of a certain inscribed cone (we analogously repeat Archimedes’ procedure) depends only on the dimension of the euclidean space and it equals to 2n/(n +1).

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

Publié en ligne: 08 Jul 2021
Pages: 211 - 230

Résumé

Abstract

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

Publié en ligne: 08 Jul 2021
Pages: 231 - 248

Résumé

Abstract

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
Accès libre

Varma Quantile Entropy Order

Publié en ligne: 08 Jul 2021
Pages: 249 - 264

Résumé

Abstract

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
Accès libre

Lp-dual three mixed quermassintegrals

Publié en ligne: 08 Jul 2021
Pages: 265 - 274

Résumé

Abstract

In the paper, the concept of Lp-dual three-mixed quermassintegrals is introduced. The formula for the Lp-dual three-mixed quermassintegrals with respect to the p-radial addition is proved. Inequalities of Lp-Minkowski, and Brunn-Minkowski type for the Lp-dual three-mixed quermassintegrals are established. The new Lp-Minkowski inequality is obtained that generalize a family of Minkowski type inequalities. The Lp-Brunn-Minkowski inequality is used to obtain a series of Brunn-Minkowski type inequalities.

Mots clés

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

MSC 2010

  • Primary 52A40
  • Secondary 46E30
15 Articles
Accès libre

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

Publié en ligne: 08 Jul 2021
Pages: 5 - 24

Résumé

Abstract

The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of c’s (depending on b). As corollary, for example, we prove that for b/2 − 1 prime, all Diophantine quadruples {2, b, c, d} with 2 < b < c < d are regular.

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.

Publié en ligne: 08 Jul 2021
Pages: 25 - 50

Résumé

Abstract

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 γ-constacyclic codes is established and the algebraic characterization of self-dual, reversible γ-constacyclic codes and γ-constacyclic codes with complementary dual are given.

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

Publié en ligne: 08 Jul 2021
Pages: 51 - 70

Résumé

Abstract

We translate some graph properties of 𝔸𝔾(R) and Γ(R) to some topological properties of Zariski topology. We prove that the facts “(1) The zero ideal of R is an anti fixed-place ideal. (2) Min(R) does not have any isolated point. (3) Rad(𝔸𝔾 (R)) = 3. (4) Rad(Γ(R)) = 3. (5) Γ(R) is triangulated (6) 𝔸𝔾 (R) is triangulated.” are equivalent. Also, we show that if the zero ideal of a ring R is a fixed-place ideal, then dtt(𝔸𝔾 (R)) = |ℬ(R)| and also if in addition |Min(R)| > 2, then dt(𝔸𝔾 (R)) = |ℬ (R)|. Finally, it is shown that dt(𝔸𝔾 (R)) is finite if and only if dtt(𝔸𝔾 (R)) is finite if and only if Min(R) is finite.

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

Publié en ligne: 08 Jul 2021
Pages: 71 - 91

Résumé

Abstract

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 x2y2m = zn

Publié en ligne: 08 Jul 2021
Pages: 93 - 105

Résumé

Abstract

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 x2y2m = zn, x, y, z, m, n ∈ ℕ, gcd(x, y) = 1, m ≥ 2, n ≥ 3.

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

Publié en ligne: 08 Jul 2021
Pages: 107 - 130

Résumé

Abstract

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

Publié en ligne: 08 Jul 2021
Pages: 131 - 154

Résumé

Abstract

In this paper we establish some two point weighted Taylor’s expansions for analytic functions f : D ⊆ ℂ→ ℂ defined on a convex domain D. Some error bounds for these expansions are also provided. Examples for the complex logarithm and the complex exponential are also given.

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

Publié en ligne: 08 Jul 2021
Pages: 155 - 171

Résumé

Abstract

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., (∈, ∈ ∨qk)-FSR(L)Is of ordered semigroup(OSG). Based on this inception, fuzzy soft level subsets are defined which link ordinary ideals with (∈, ∈ ∨qk)-fuzzy soft left(right) ideals. Some binary operations like ◦λ, intersection ∩λ and union of fuzzy soft sets ∪λ are given and various fundamental results of ideal theory are developed through these types of fuzzy soft ideals.

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

Publié en ligne: 08 Jul 2021
Pages: 173 - 186

Résumé

Abstract

Let R be a commutative ring with identity and S be a multiplicative subset of R. In this paper, we introduce the concept of weakly S-prime ideals which is a generalization of weakly prime ideals. Let P be an ideal of R disjoint with S. We say that P is a weakly S-prime ideal of R if there exists an sS such that, for all a, bR, if 0 ≠ abP, then saP or sbP. We show that weakly S-prime ideals have many analog properties to these of weakly prime ideals. We also use this new class of ideals to characterize S-Noetherian rings and S-principal ideal rings.

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

Publié en ligne: 08 Jul 2021
Pages: 187 - 198

Résumé

Abstract

We show a simple example for ordered semigroup 𝕊 = 𝕊 (+,⩽) that 𝕊 ⊆ℝ (ℝ denotes the real line) and ]a, b[ + ]c, d[ = ]a + c, b + d[ for all a, b, c, d ∈ 𝕊 such that a < b and c < d, but the intervals are no translation invariant, that is, the equation c +]a, b[ = ]c + a, c + b[ is not always fulfilled for all elements a, b, c ∈ 𝕊 such that a < b.

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 Ix := {1, 2, . . ., x} for all x ∈ ℤ+ and defined the function g : ℤ+ → ℤ+ by g(x):=max{ y+|IyIxIx } g\left( x \right): = \max \left\{ {y \in {\mathbb{Z}_ + }|{I_y} \subseteq {I_x} \cdot {I_x}} \right\} for all x ∈ ℤ+. We give the function g implicitly using the famous Theorem of Chebishev.

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

Publié en ligne: 08 Jul 2021
Pages: 199 - 209

Résumé

Abstract

Archimedes’ well known theorem on the area of a parabolic segment says that this area is 4/3 of the area of a certain inscribed triangle. In this paper we generalize this theorem to the n-dimensional euclidean space, n ≥ 3. It appears that the ratio of the volume of an n-dimensional solid bounded by an (n − 1)-dimensional hyper-paraboloid and an (n − 1)-dimensional hyperplane and the volume of a certain inscribed cone (we analogously repeat Archimedes’ procedure) depends only on the dimension of the euclidean space and it equals to 2n/(n +1).

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

Publié en ligne: 08 Jul 2021
Pages: 211 - 230

Résumé

Abstract

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

Publié en ligne: 08 Jul 2021
Pages: 231 - 248

Résumé

Abstract

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
Accès libre

Varma Quantile Entropy Order

Publié en ligne: 08 Jul 2021
Pages: 249 - 264

Résumé

Abstract

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
Accès libre

Lp-dual three mixed quermassintegrals

Publié en ligne: 08 Jul 2021
Pages: 265 - 274

Résumé

Abstract

In the paper, the concept of Lp-dual three-mixed quermassintegrals is introduced. The formula for the Lp-dual three-mixed quermassintegrals with respect to the p-radial addition is proved. Inequalities of Lp-Minkowski, and Brunn-Minkowski type for the Lp-dual three-mixed quermassintegrals are established. The new Lp-Minkowski inequality is obtained that generalize a family of Minkowski type inequalities. The Lp-Brunn-Minkowski inequality is used to obtain a series of Brunn-Minkowski type inequalities.

Mots clés

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

MSC 2010

  • Primary 52A40
  • Secondary 46E30

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