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Advances in Pure Mathematics (APM) is an openly accessible journal published monthly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of ordered algebraic structures. All the manus…
Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger, Dennis Spellman
The Tarski theorems, proved by Myasnikov and Kharlampovich and inde-pendently by Sela say that all nonabelian free groups satisfy the same first-order or elementary theory. Kharlampovich and Myasnikov also prove that the elementary theory of free groups is de…
Eugene Demidenko
Symmetric circulant matrices (or shortly symmetric circulants) are a very special class of matrices sometimes arising in problems of discrete periodic convolutions with symmetric kernel. First, we collect major properties of symmetric circulants scattered thr…
Toshiyuki Kohno
Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is proved. And the convergence and compariso…
Daniel C. Mayer
Let p be a prime and K be a number field with non-trivial p -class group Cl p K . A crucial step in identifying the Galois group G ∞ p of the maximal unramified pro- p extension of K is to determine its two-stage approximation M=G 2 p k, that is the second de…
Leo Depuydt
The number circle—that is, the notion that the largest possible positive numbers are followed by infinity and then by the smallest possible negative numbers—is not new. L. Euler defended it in the eighteenth century and, before him, J. Wallis considered somet…
Sisu Li, Wanzhou Ye
This paper presents an accurate and efficient algorithm for solving the generalized elastic net regularization problem with smoothed l 0 penalty for recovering sparse vector. Finding the optimal solution to the unconstrained l 0 minimization problem in the re…
Ning Mao, Wanzhou Ye
Considering the problem of feature selection in linear regression model, a new method called LqCP is proposed simultaneously to select variables and favor a grouping effect, where strongly correlated predictors tend to be in or out of the model together. LqCP…
Paul Bracken
Short Retraction Notice The paper does not meet the standards of "Advances in Pure Mathematics". This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines . The aim is t…
Paul Bracken
An important question that arises is which surfaces in three-space admit a mean curvature preserving isometry which is not an isometry of the whole space. This leads to a class of surface known as a Bonnet surface in which the number of noncongruent immersion…
Lin Xia, Xudong Huang, Guanpeng Wang, Tao Wu
The positive-definiteness and sparsity are the most important property of high-dimensional precision matrices. To better achieve those property, this paper uses a sparse lasso penalized D-trace loss under the positive-definiteness constraint to estimate high-…
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Advances in Pure Mathematics (APM) is an openly accessible journal published monthly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of ordered algebraic structures. All the manus… All articles are open access under a CC BY 4.0 licence, with authors retaining copyright.
Authors submit their manuscript, metadata, and declarations through the portal. There is no submission fee.
The editorial office screens the manuscript for scope, completeness, and formatting before assigning a handling editor.
At least two independent reviewers evaluate the manuscript under single-blind review. Where revisions are required, authors respond point by point.
On acceptance the article processing charge is invoiced and the CC BY 4.0 copyright handover is signed.
The article is copyedited, typeset, and given a DOI, then publishes open access with a permanent link.
Manuscripts must be original and not under consideration elsewhere. Submit in Microsoft Word or LaTeX with figures at 300 dpi minimum. Structure research articles as Abstract, Introduction, Methods, Results, Discussion, and References.
Use the journal's numbered (Vancouver) reference style. Cite sources consecutively in the order they appear, and ensure every reference is complete and retrievable.
Declare all funding sources, conflicts of interest, and ethical approvals (including informed consent and animal-care statements where applicable).