Mathematical Papers Research Articles

Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension

Let p be an odd prime and let r be the smallest generator of the multiplicative group Zp∗. We show that there exists a correlation of size Θ(r2) that self-tests a maximally entangled state of local dimension p−1. The construction of the correlation uses the embedding procedure proposed by Slofstra (Forum of Mathematics, Pi. (2019)). Since there are infinitely many prime numbers whose smallest multiplicative generator is in the set {2,3,5} (D.R. Heath-Brown The Quarterly Journal of Mathematics (1986) and M. Murty The Mathematical Intelligencer (1988)), our result implies that constant-sized correlations are sufficient for self-testing of maximally entangled states with unbounded local dimension.

A New Generalized Quasi-Newton Algorithm Based on Structured Diagonal Hessian Approximation for Solving Nonlinear Least-Squares Problems With Application to 3DOF Planar Robot Arm Manipulator

Many problems in science and engineering can be formulated as nonlinear least-squares (NLS) problems. Thus, the need for efficient algorithms to solve these problems can not be overemphasized. In that sense, we introduce a generalized structured-based diagonal Hessian algorithm for solving NLS problems. The formulation associated with this algorithm is essentially a generalization of a similar result in Yahaya <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (Journal of Computational and Applied Mathematics, pp. 113582, 2021). However, in this work, the structured diagonal Hessian update is derived under a weighted Frobenius norm; this allows other choices of the weighted matrix analogous to the Davidon-Fletcher-Powell (DFP) method. Moreover, to theoretically fill the gap in Yahaya <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (Journal of Computational and Applied Mathematics, pp. 113582, 2021), we have shown that the proposed algorithm is R-linearly convergent under some standard conditions devoid of any safeguarding strategy. Furthermore, we experimentally tested the proposed scheme on some standard benchmark problems in the literature. Finally, we applied this algorithm to solve robotic motion control problem consisting of 3DOF (degrees of freedom).

RELAXED MODULUS-BASED SYNCHRONOUS MULTISPLITTING MULTI-PARAMETERS TOR (TWO-PARAMETERS OVER-RELAXATION) METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

In 2013, Bai and Zhang [<i>Numerical Linear Algebra with Applications</i>, 20(2013):425-439] constructed modulus-based synchronous multisplitting methods by an equivalent reformulation of the linear complementarity problems into a system of fixed-point equations and studied the convergence of them. In 2014, Zhang and Li [<i>Computers and Mathematics with Application</i>, 67(2014):1954-1959] analyzed and obtained the weaker convergence results for linear complementarity problems. In 2008, Zhang et.al. [<i>International Journal of Computer Mathematics</i>, 85(2)(2008):211-224] presented global relaxed non-stationary multisplitting multi-parameter method by introducing some relaxed parameters. In this paper, we generalize Bai and Zhang's methods and study relaxed modulus-based synchronous multisplitting multi-parameters TOR (two-parameters over-relaxation, abbreviated as TOR) methods for linear complementarity problems. Furthermore, the convergence results of our new method in this paper are given when the system matrix is an $H_{+}-$matrix.

Approximation properties by some modified Szasz-Mirakjan-Kantorovich operators

The present article deals with the local approximation results by means of Lipschitz maximal function, Ditzian-Totik modulus of smoothness and Lipschitz type space having two parameters for the summation-integral type operators defined by Mishra and Yadav (Tbilisi Mathematical Journal. 11(3), (2018), 175-91). Further, we determine the rate of convergence in the term of the with derivative of bounded variation and for the quantitative means of the defined operators, we establish the quantitative Voronovskaya type and Gr$\ddot{\text{u}}$ss type theorems. Moreover, the examples are given with graphical representation to support the main results.

RETRACTED : Aplikasi nanokomposit silika Aerogel-Karbon aktif sebagai adsorben Rhodamin-B

Following a rigorous, carefully concerns and considered review of the article published in Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) to article entitle "Aplikasi nanokomposit silika Aerogel-Karbon aktif sebagai adsorben Rhodamin-B" Vol. 2 No. 2 (2022).This paper has been found to be in violation of the Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) publication principles and has been retracted.The article contained redundant material, the editor investigated and found that the paper published in AIP Conference ProceedingsThe document and its content has been removed from Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) and reasnable effort should be made to remove all references to this article.

RETRACTED : Nanopartikel magnetit termodifikasi asam salisilat dan aplikasinya sebagai adsorben malasit hijau

Following a rigorous, carefully concerns and considered review of the article published in Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) to article entitle "Nanopartikel magnetit termodifikasi asam salisilat dan aplikasinya sebagai adsorben malasit hijau" Vol. 2 No. 2 (2022).This paper has been found to be in violation of the Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) publication principles and has been retracted.The article contained redundant material, the editor investigated and found that the paper published in AIP Conference ProceedingsThe document and its content has been removed from Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) and reasnable effort should be made to remove all references to this article.

RETRACTED : Sintesis dan karakterisasi nanokomposit silika aerogel−karbon aktif

Following a rigorous, carefully concerns and considered review of the article published in Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) to article entitle "SINTESIS DAN KARAKTERISASI NANOKOMPOSIT SILIKA AEROGEL−KARBON AKTIF" Vol. 2 No. 2 (2022).This paper has been found to be in violation of the Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) publication principles and has been retracted.The article contained redundant material, the editor investigated and found that the paper published in AIP Conference ProceedingsThe document and its content has been removed from Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) and reasnable effort should be made to remove all references to this article.

RETRACTED : Karakterisasi campuran karagenan-gellan gum dan aplikasinya sebagai matriks tablet lepas lambat

Following a rigorous, carefully concerns and considered review of the article published in Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) to article entitle "Karakterisasi campuran karagenan-gellan gum dan aplikasinya sebagai matriks tablet lepas lambat" Vol. 2 No. 2 (2022).This paper has been found to be in violation of the Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) publication principles and has been retracted.The article contained redundant material, the editor investigated and found that the paper published in ICOMSEThe document and its content has been removed from Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) and reasnable effort should be made to remove all references to this article.

RETRACTED : Kajian adsorpsi, pengaruh humat dan fulvat, serta desorpsi ion Ni2+ dan Cd2+ menggunakan kompos TPA Tlekung

Following a rigorous, carefully concerns and considered review of the article published in Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) to article entitle "Kajian adsorpsi, pengaruh humat dan fulvat, serta desorpsi ion Ni2+ dan Cd2+ menggunakan kompos TPA Tlekung" Vol. 2 No. 2 (2022).This paper has been found to be in violation of the Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) publication principles and has been retracted.The article contained redundant material, the editor investigated and found that the paper published in ICOMSEThe document and its content has been removed from Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) and reasnable effort should be made to remove all references to this article.

RETRACTED : Pengembangan media pembelajaran SOP (simulation of proportion) : sticker book berbasis simulasi pada materi perbandingan senilai dan berbalik nilai

Following a rigorous, carefully concerns and considered review of the article published in Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) on this article. This paper has been found to be in violation of the Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) publication principles and has been retracted.The article contained redundant material, the editor investigated and found that the paper published in other academic publishing platforms. The document and its content has been removed from Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) and reasnable effort should be made to remove all references to this article.

RETRACTED : Pengembangan multimedia interaktif pada materi bangun ruang sisi datar untuk siswa SMP kelas VIII

Following a rigorous, carefully concerns and considered review of the article published in Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) on this article. This paper has been found to be in violation of the Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) publication principles and has been retracted.The article contained redundant material, the editor investigated and found that the paper published in other academic publishing platforms. The document and its content has been removed from Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) and reasnable effort should be made to remove all references to this article.

Normalized fractional inequalities for continuous random variables

We introduce new normalized fractional integral concepts on random variables. We also introduce the fractional coupled random variables. The Jensen integral inequality is generalized. Also, some fractional bounds estimating the expectation and variance are delivered. At the end, some other results related to the coupled random variables are proved. For this work, some results of the papers [On some statistical and probability inequalities. Journal of Inequalities and Special Functions, 2016] and [Some inequalities for the expectation and variance of a random variable whose PDFs are absolutely continuous using a pre-Chebychev inequality. Tamkang Journal of Mathematics, 2001] are deduced as some special cases.

RETRACTED : Pengembangan instrumen asesmen dan survei literasi kimia peserta didik SMA kelas XI pada materi larutan penyangga

Following a rigorous, carefully concerns and considered review of the article published in Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) to article entitle "Pengembangan instrumen asesmen dan survei literasi kimia peserta didik SMA kelas XI pada materi larutan penyangga" Vol. 1 No. 6 (2021) This paper has been found to be in violation of the Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) publication principles and has been retracted.The article contained redundant material, the editor investigated and found that the paper published in AIP Conference Proceedings 2215, 020013 (2020) The document and its content has been removed from Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) and reas

RETRACTED : Pengembangan instrumen asesmen literasi kimia pilihan ganda materi asam basa

Following a rigorous, carefully concerns and considered review of the article published in Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) to article entitle "Pengembangan instrumen asesmen literasi kimia pilihan ganda materi asam basa" Vol. 1 No. 6 (2021)This paper has been found to be in violation of the Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) publication principles and has been retracted.The article contained redundant material, the editor investigated and found that the paper published in AIP Conference ProceedingsThe document and its content has been removed from Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) and reasnable effort should be made to remove all references to this article.

RETRACTED : Pengaruh strategi pembelajaran metakognitif preparing, doing, checking, dan assessing and following-up (PDCA) terhadap pengetahuan metakognitif dan prestasi belajar peserta didik kelas X MIPA SMAN 1 Turen pada materi larutan elektrolit dan non elektrolit

Following a rigorous, carefully concerns and considered review of the article published in Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) to article entitle "Pengaruh strategi pembelajaran metakognitif preparing, doing, checking, dan assessing and following-up (PDCA) terhadap pengetahuan metakognitif dan prestasi belajar peserta didik kelas X MIPA SMAN 1 Turen pada materi larutan elektrolit dan non elektrolit" Vol. 1 No. 6 (2021). This paper has been found to be in violation of the Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) publication principles and has been retracted.The article contained redundant material, the editor investigated and found that the paper published in ICOMSE The document and its content has been removed from Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) and reasnable effort should be made to remove all references to this article.

Solstice: An Electronic Journal of Geography and Mathematics: Vol. 32, No. 1

Solstice: An Electronic Journal of Geography and Mathematics: Vol. 32, No. 1

Normed Ideal Perturbation of Irreducible Operators in Semifinite Von Neumann Factors

An interesting result proved by Halmos in Hal (Michigan Mathematical Journal, 15, 215–223 (1968) is that the set of irreducible operators is dense in \({\mathcal {B}}({\mathcal {H}})\) in the sense of Hilbert-Schmidt approximation. In a von Neumann algebra \({\mathcal {M}}\) with separable predual, an operator \(a\in {\mathcal {M}}\) is said to be irreducible in \({\mathcal {M}}\) if \(W^*(a)\) is an irreducible subfactor of \({\mathcal {M}}\), i.e., \(W^*(a)'\cap {\mathcal {M}}={{\mathbb {C}}} \cdot I\). Let \(\Phi (\cdot )\) be a \(\Vert \cdot \Vert \)-dominating, unitarily invariant norm (see Definition 2.1). Many well-known norms are of this type such as the operator norm \(\Vert \cdot \Vert \) and the \(\max \{\Vert \cdot \Vert , \Vert \cdot \Vert _p\}\)-norm (for each \(p>1\)). In Theorem 3.1, we prove that in every semifinite factor \({\mathcal {M}}\) with separable predual, if the norm \(\Phi (\cdot )\) satisfies a natural condition introduced in (1.1), then irreducible operators are \(\Phi (\cdot )\)-norm dense in \({\mathcal {M}}\). In particular, the operator norm \(\Vert \cdot \Vert \) and the \(\max \{\Vert \cdot \Vert , \Vert \cdot \Vert _p\}\)-norm (for each \(p>1\)) naturally satisfy the condition in (1.1). This can be viewed as a (stronger) analogue of a theorem of Halmos in Hal (Michigan Mathematical Journal, 15, 215–223 (1968), proved with different techniques developed in semifinite, properly infinite factors with separable predual. It is natural to ask whether the condition in (1.1) is necessary for Theorem 3.1. We prove that the condition in (1.1) is not necessary for normal operators. In Theorem 4.1, for every \(\Vert \cdot \Vert \)-dominating, unitarily invariant norm \(\Phi (\cdot )\), we develop another method to prove that each normal operator in \({\mathcal {M}}\) is a sum of an irreducible operator in \({\mathcal {M}}\) and an arbitrarily small \(\Phi (\cdot )\)-norm perturbation. Particularly, the \(\Phi (\cdot )\)-norm can be the trace class norm \( \Vert \cdot \Vert _1\) on the set of trace class operators in \({\mathcal {B}}({\mathcal {H}})\).

RETRACTED : Pengembangan tes penjelasan ilmiah materi sistem ekskresi manusia untuk siswa SMP/MTs kelas VIII

Following a rigorous, carefully concerns and considered review of the article published in Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) to article entitle "Pengembangan tes penjelasan ilmiah materi sistem ekskresi manusia untuk siswa SMP/MTs kelas VIII" Vol. 1 No. 5 (2021) This paper has been found to be in violation of the Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) publication principles and has been retracted. The article contained redundant material, the editor investigated and found that the paper published in AIP Conference Proceedings 2215, 020013 (2020) The document and its content has been removed from Jurnal MIPA dan Pembelajarannya (Journal of Mathematics, Science, and Instruction) and reasnable effort should be made to remove all references to this article.

Binary Sequences Derived from Dickson Permutation Polynomials over Binary Extension Field

In this paper, based on a result of Lidl and Mullen (Mathematical Journal of Okayama University, 1991), the maximum length and the second maximum length that can be attained by cycles of Dickson permutation polynomial (of the first kind) with parameter 1 are studied. Necessary and sufficient conditions for these two lengths to be attained are given, which are connected with Fermat primes and Mersenne primes, respectively. Furthermore, a class of coordinate sequences that maintains a large period is obtained, which is shown to be the coordinate sequences derived from cycles of the second maximum length. Explicit formulas for their periodicity and shift-equivalences are also presented.

Some remarks on fuzzy infi topological spaces

Induced fuzzy infi topological space is already introduced by Saha and Bhattacharya [Saha A.K., Bhattacharya D. 2015, Normal Induced Fuzzy Topological Spaces, Italian Journal of Pure and Applied Mathematics, 34, 45-56]. In this paper for the said space, we further analyse some properties viz. fuzzy I-continuity, fuzzy infi open mappings and fuzzy infi closed mappings etc. Also we study product fuzzy infi topological space and establish some results concerned with it.