NA Digest, V. 19, # 23

NA Digest Sunday, June 09, 2019 Volume 19 : Issue 23

Today's Editor:

Daniel M. Dunlavy
Sandia National Labs

Today's Topics: Subscribe, unsubscribe, change address, or for na-digest archives:

Submissions for NA Digest:

From: Nick Trefethen
Date: June 05, 2019
Subject: History of least-squares boundary matching for PDEs

Can NA Digest readers help me with a bit of history? In a Stanford
technical report of 1969 (,
Cleve Moler recommended least-squares fitting on the boundary as a
method for solving Laplace problems. It seems unlikely this could
have been the first use of least-squares boundary matching for PDEs,
but can somebody point me to anything earlier?

This question is part of a larger story, I believe, of a transition
from square to rectangular thinking in a number of computational
areas. When Householder proposed reflectors for QR factorization in
1958, for example, his matrices were square; only later did many of us
come to regard the "skinny" variant as more fundamental. For years
people investigating problems of infinite matrices mainly used a
square rather than rectangular "finite section method." Approximation
theorists put great effort into methods based on interpolation rather
than least-squares (Fekete points, Lebesgue constants,...). In
Fourier analysis we had centuries of attention to bases before people
started talking about redundant bases and frames. And so on into this
era of data science, where rectangular seems often more natural than

From: Robert van de Geijn
Date: June 08, 2019
Subject: MOOC, Programming for High Performance, now in session

A few weeks ago we announced that "LAFF-On Programming for High
Performance" [1] was open for registration. This free-to-audit,
four-week course developed by UT-Austin faculty Robert van de Geijn,
Maggie Myers, and Devangi Parikh is now in session.

This course exposes techniques for attaining high performance through
carefully scaffolded exercises that illustrate how the BLAS-like
Library Instantiation Software (BLIS) [2] and other such libraries
implement matrix-matrix multiplication based on Goto's algorithm [3].
Topics span instruction-level parallelism via vector intrinsic
functions, reusing data in caches, and multithreaded parallelization
via OpenMP.

We believe this course is appropriate for a novice yet of interest to
an expert.

Please help us spread the word!


[2] Field G. Van Zee, Robert A. van de Geijn. BLIS: A Framework for
Rapidly Instantiating BLAS Functionality. ACM TOMS, 2015.

[3] Kazushige Goto, Robert A. van de Geijn. Anatomy of
high-performance matrix multiplication. ACM TOMS, 2008.

From: Field G. Van Zee
Date: June 06, 2019
Subject: BLIS 0.6.0 now available

The Science of High-Performance Computing (SHPC) research group at The
University of Texas at Austin is pleased to announce BLIS 0.6.0, made
possible thanks to our partnership with AMD.

BLIS is a software framework for rapidly instantiating high-
performance BLAS-like dense linear algebra operations. Aside from
being a developer's tool, the framework also allows end-users to build
libraries that implement a superset of the BLAS, which can be called
via conventional BLAS-like or object APIs, or via standard BLAS
interfaces. (An optional CBLAS API is also available.)

BLIS 0.6.0 provides accelerated dgemm on small/skinny matrix problems
for a wide range of modern microarchitectures, including Intel Haswell
through Coffee Lake and AMD Zen-based Ryzen/Epyc. AMD's upcoming Zen2-
based Ryzen/Epyc will also be supported. For now, this class of small
matrix problems is only optimized for double-precision real gemm.
Similarly, the new implementation does not yet support multithreaded
parallelism. Still, measured speedup for problems with at least one
dimension exceedingly small (e.g. m = 6) is dramatic. Performance
results are illustrated on two systems--an Intel Kaby Lake and an AMD
Epyc--in a new markdown document available via the web [1] as well as
the BLIS source distribution.

For other links to code, documentation, mailing lists, publications,
and related information, please visit the BLIS github website [2].


From: Toby Driscoll
Date: June 07, 2019
Subject: Python codes for NA/scicomp textbook

I have translated into Python all 45 functions and 160+ examples from
the textbook Fundamentals of Numerical Computation (SIAM), co-authored
by Rich Braun and myself.

Book website:
New codes:

The text and codes cover at an advanced undergraduate level the basics
of dense matrix factorizations, rootfinding and nonlinear
least-squares, interpolation, initial-value problems, EVD and SVD,
Krylov iterations, boundary-value problems, and the method of lines
for PDEs.

The codes require nothing beyond Python 3, scipy, and numpy, and
matplotlib. They complement the previously supplied Julia and original
MATLAB versions of the codes.

From: Kris ONeill
Date: June 05, 2019
Subject: New Book, A Mathematical Introduction to Electronic Structure Theory

A Mathematical Introduction to Electronic Structure Theory
By Lin Lin and Jianfeng Lu

Based on first principle quantum mechanics, electronic structure
theory is widely used in physics, chemistry, materials science, and
related fields and has recently received increasing research attention
in applied and computational mathematics. This book provides a
self-contained, mathematically oriented introduction to the subject
and its associated algorithms and analysis. It will help applied
mathematics students and researchers with minimal background in
physics understand the basics of electronic structure theory and
prepare them to conduct research in this area. The book is written for
advanced undergraduate and beginning graduate students, specifically
those with mathematical backgrounds but without a priori knowledge of
quantum mechanics, and can be used for self-study by researchers,
instructors, and other scientists

2019 / x + 127 pages / Softcover / 978-1-611975-79-6 / List $44.00 /
SIAM Member $30.80 / SL04

See more details here:

From: Gabriele Steidl
Date: June 03, 2019
Subject: New Book, Numerical Fourier Analysis

Numerical Fourier Analysis
Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
Birkhauser, Basel 2018

This book encompasses the required classical Fourier theory in the
first part in order to give deep insight into the construction and
analysis of corresponding fast Fourier algorithms in the second part,
including recent developments on non-equispaced and sparse FFTs in
higher dimensions, and spherical Fourier transforms. In the third
part of the book contains a selection of applications, in particular
research results on non-linear function approximation by exponential
sums (Prony methods).

See more details here:

From: Anne Reinarz
Date: June 09, 2019
Subject: ExaHyPE User Workshop, Germany, Jul 2019

ExaHyPE - Solving Hyperbolic PDEs with high-order DG

ExaHyPE ( is an open source simulation engine to solve
systems of hyperbolic equation systems. For the 2nd workshop, we again
invite existing users and interested potential users alike to join us
for four days. Users can try out the engine while some developers are
around, i.e. they start the week with a problem given as PDE in mind
and go home with a working first prototype built on top of ExaHyPE.

The workshop takes place at the Leibniz Supercomputing Centre in
Garching from the 22 July 2019 until Fri, 26 July.

Registration at: We can
provide a limited number of travel grants to European partners.

From: Rene Caspart
Date: June 04, 2019
Subject: The Art of Data, Germany, Aug 2019

We are pleased to announce that the registration of the 17th
International GridKa School 2019 "The Art of Data" has been opened.

The GridKa School will take place from August, 26th to 30th at the
Karlsruhe Institute of Technology, Germany.

This year's school will again impart knowledge using a mixture of
plenary talks and hands-on courses focusing on interesting and
state-of-the-art topics in workflow management, modern programming,
and data analytics. Topics are for example: Machine Learning, GoLang,
Rustlang, Embedded Programming, Pandas and Dask, Concurrent
Programming, GPUs, High Performance Computing, Docker, (No)SQL,
HTCondor, Quantum Computing, the Elastic Stack and much more.

Please visit our web site for more details and for the preliminary agenda and

- Early bird registration with reduced fees is available until
July, 15th.
- Pre-booked hotel room contingent expires on July, 15th.
- School dates: August, 26th - August, 30th.

In case you have additional questions, please feel free to contact us

From: khalide jbilou
Date: June 06, 2019
Subject: Mathematical Modeling for Complex Systems, Morocco, Apr 2020

Mathematical Modeling for Complex Systems (M2CS)
Cadi Ayyad University, Marrakech Morocco
April, 6--9, 2020

The conference is dedicated to Professor Hassane Sadok for his 60th

Main Topics:
- Large linear systems and preconditioning, eigenvalue
- problems. Linear algebra and control, model reduction. Ill-posed
- problems, Image processing. Numerical methods for PDEs.
- Approximation, Optimisation. Applied Statistics.
- Applications: Artificial Intelligence- Data Mining - Machine
Learning- Image processing

Plenary Speakers: M. Benzi (Italy), C. Brezinski (France), F. Dopico
(Spain); G. Meurant (France); M. Mitrouli (Greece); M. Raydan
(Portugal); L. Reichel (USA) ; Y. Saad (USA); H. Sadok (France);
P. Van Dooren (Belgium).

Important Dates:
January 15, 2020 - Deadline for submission of titles and abstracts
February 1, 2020 - Deadline for registration

The proceedings of the conference will appear as a special volume of
an international journal.

For more informations, please refer to the web page: or contact us at:

From: Lajmi Lakhal-Chaieb
Date: June 06, 2019
Subject: Tenure-track Position, Applied Mathematics

Tenure track position in Applied Mathematics

The Department of Mathematics and Statistics of Universite Laval
invites applications for a tenure track position in applied
mathematics. Preference will be given to candidates presenting a
research program in analysis and numerical solutions of partial
differential equations. Candidates with a Ph.D. (or on the verge of
obtaining one) in applied mathematics or a close related field are
invited to present their candidacy. Hiring will normally be at the
rank of assistant professor and the appointment would start in January 2020.

The successful candidate will be expected to recruit and supervise
graduate students, engage in a productive research program, apply for
funding from the major granting bodies, teach in French undergraduate
and graduate applied mathematics courses (including large class
service courses), contribute to the management and promotion of
departmental programs, and more generally contribute to the
development and day-to-day functioning of the Department. Selection
criteria. Candidates must have obtained a PhD degree in applied
mathematics, or an equivalent qualification, or hold a PhD in a
neighboring area with a strong expertise in applied mathematics, be
able to propose an independent research program for which the
candidate could rapidly obtain adequate funding, be able to contribute
to the strong industry oriented research activities of the applied
mathematics group of the DMS, demonstrate the potential to recruit and
supervise graduate students in applied mathematics, demonstrate the
capacity and interest to teach and maintain applied mathematics
courses, at the undergraduate and graduate levels, including large
class service courses, demonstrate excellent pedagogical abilities to
teach and create applied matthematics courses for students in
mathematics, as well as students in other programs, be able to teach
in French or be able to do so within a year. Applications must include
a CV, three letters of reference (ideally including one addressing
teaching experience or potential), an outline of research plans for
the next three years (3 pages maximum), a teaching philosophy
statement (2 pages maximum), and up to three recent articles
(preprints or off-prints). The candidate should clearly indicate
his/her level of French proficiency and comment on his/her capacity to
become proficient within one year.

Application may be submitted through Mathjobs
(, by e-mail (in pdf) to, or by regular mail to
Poste en mathematiques appliquees
Departement de mathematiques et de statistique
1045, av. de la Medecine
Universite Laval
Quebec (Quebec)
Canada G1V 0A6

Applications must be received by July 31, 2019.

For more information, please contact the department chair,

From: Jochen Schuetz
Date: June 04, 2019
Subject: Lecturer Position, Computational Mathematics

UHasselt seeks lecturer in Computational Mathematics.

You will strengthen and extend the research capacity of the group
Computational Mathematics (CMAT), both from a methodological point of
view as well as the domain of applications. Inspired by real-life
applications, the research in this group is mainly oriented towards
numerical analysis and simulation of (partial) differential equations,
including multiple scales (see Examples
of research areas are stochastic differential equations, data
assimilation and uncertainty quantification, inverse problems,
optimization, or model order reduction.

Multidisciplinary collaboration is expected with the research in
computational and applied mathematics, as well as within and outside
the faculty and Hasselt University.

More information can be found on

From: Julia Brandt
Date: June 05, 2019
Subject: Research Fellow Position, Germany

Job Description: Scientific services in the research project
"Equilibria for Energy Markets with Transport" (Cluster of Excellence
MATH+); the research will concentrate on modeling, analytic,
optimization and numerical aspects of generalized Nash equilibrium
problems with partial differential equation constraints; tasks for own
scientific qualification (doctorate)

Requirements: A completed university degree in mathematics or a
related discipline (preferably with very good results); Knowledge of
continuous optimization and applied functional analysis; Experience in
the field of numerical and computer-aided implementation; a high
proficiency in spoken and written English

For further information see: or

Please send your application until June 19, 2019 and quoting the
reference number DR/100/19 to Humboldt-Universitat zu Berlin, Faculty
of Mathematics and Natural Sciences, Department of Mathematics,
Prof. Dr. Michael Hintermuller (located: Rudower Chaussee 25), Unter
den Linden 6, 10099 Berlin, or preferably in electronic form to (cc to

The Humboldt-Universitat is seeking to increase the proportion of
women in research and teaching, and specifically encourages qualified
female scholars to apply. Severely disabled applicants with equivalent
qualifications will be given preferential consideration. People with
an immigration background are specifically encouraged to apply. Since
we will not return your documents, please submit copies in the
application only.

Please visit our website, which gives
you access to the legally binding German version.

From: Miguel A. Benítez
Date: June 03, 2019
Subject: Research Technician Positions, BCAM

IC2019_KTU CFD Research Technician: Computational Fluid Dynamics
(CFD): Finite Volume Methods (FVM), Finite Element Methods (FEM) or
Smoothed Particle Hydrodynamics (SPH). Numerical methods for soling
compressible and incompressible flows and multi-phase
simulations. Eulearian and Lagrangian fluid models, CFD applied to
Advanced Manufacturing (Industry 4.0), Energy Sector or Biomedical


IC2019_KTU Data Science Research Technician: Statistics (regression
methods, time series, survival analysis, multivariate analysis,
clustering methods), Machine Learning techniques (e.g.: neural
networks, random forests, decision trees, etc.).


About BCAM Knowledge Transfer Unit (KTU): The aim of the KTU is to
develop mathematical solutions for scientific challenges based on
real- life applications. One of BCAM's most important missions is to
spread knowledge and technology in the industry and the society in
general. It is critical for the Basque Center for Applied Mathematics
to transfer the obtained research results to sectors as biosciences,
health, energy, advanced manufacturing, telecommunications and
transport, including local, national and international entities. For
further information, please visit the website: BCAM KTU

From: H. Metin Aktulga
Date: June 03, 2019
Subject: Postdoc Position, HPC & Molecular Dynamics, Michigan State Univ

The Department of Computer Science and Engineering (CSE) invites
applications from outstanding candidates for a fixed term research
associate position in the areas of molecular dynamics and high
performance computing (HPC). The successful candidate will be
supervised by Prof. Aktulga (CSE) and Prof. Merz (Chemistry). The
duties include (but are not limited to)
- development of hybrid reactive/classical MD models and software,
- application of hybrid reactive/classical MD to metalloproteins,
- performance optimization of resulting software for multicore and/or
GPU clusters.

Interested applicants can submit their applications at MSU's Career

From: Alfredo Buttari
Date: June 03, 2019
Subject: Postdoc Position, Parallel Sparse Linear Solvers, IRIT Toulouse

We are seeking candidates for a 18-months post-doctoral position at
the IRIT laboratory of Toulouse (France). The subject is related to
the improvement of methods for the solution of sparse linear systems
on large scale parallel supercomputers. Specifically, this post-doc
will investigate methods for reducing the complexity and improving the
scalability of multigrid solvers through the use of low-rank
approximation techniques in the coarse grid solver or in the
intermediate levels smoothers.

The successful candidate will work in the context of the European
EoCoE-II project ( whose objective is to
leverage the potential offered by the ever-growing computing
infrastructure to foster and accelerate the European transition to a
reliable low carbon energy supply using High Performance Computing.

Requirements: PhD in Computer Science or Mathematics, strong expertise
in sparse linear algebra and high performance parallel computing.

Detailed information:

Contact: Alfredo Buttari (

From: Christine Shoemaker
Date: June 02, 2019
Subject: Postdoc Positions, Computational Optimization, Nat'l Univ. of Singapore

Job Requirements: (English is the language for Singapore and NUS)
1) a. PhD in Operations Research, ISE, Applied Mathematics, ,Computer
Science or from similar programs. 2) extensive experience in
developing complex computer codes, preferably in Python or C++. 3)
Ability to construct and write papers for leading research journals
and conferences in English. It is an advantage, but not a requirement
for a candidate to have expertise in any of the following areas:
surrogates, distributed computing, algorithm proofs, machine learning,
uncertainty quantification, numerical analysis). If candidate has
prior optimization (e.g. nonlinear programming) experience, prior
knowledge of surrogate global optimization is not required.

Research Focus and Goals: Postdoc will work with Prof. Shoemaker's
group ( a mixture of OR, CS, and Statistics PHD's) to develop serial
and parallel optimization algorithms . The candidate will have
expenses paid to present at international conferences and can work on
the new Singapore Supercomputer (NSCC).

JOB: Appointment is at least 18 months, with extension possible . The
salary and benefits (and health care) are internationally competitive

Application: Send Prof. Shoemaker at a cover
letter, a CV & desired start time. Put "Postdoc 2019 opt" in the email
subject line. Review of applications will begin immediately and
continue until the positions are filled. Candidates will be considered
who would like to start as soon as possible as well as those who
cannot begin for many months.

Supervisor: Distinguished Professor Shoemaker (PhD in mathematics,
member of the US National Academy of Engineering and Fellow in the
following: SIAM, INFORMS, AGU, ASCE) was Ripley Professor at Cornell
University in US before coming to National University of Singapore.
She is co-author (with Eriksson and Prof. Bindel)) of open source
surrogate global optimization toolbox "pySOT" in GitHub (which has had
over 70,000 downloads). More information at and .

From: J. Lu
Date: June 06, 2019
Subject: Postdoc Positions, Computer Vision/Optimization/Inv Problems, Shenzhen Univ

Postdoc Positions in Shenzhen University, China
Location: Shenzhen, China
Job Type: Full-Time
Duration: 2 years
Number of Position: 4 Positions
Closing Date: Open Until Filled

Description: We are looking for Postdoctoral Researchers in
Image/Video Processing/Analysis,Mathematical Imaging, Computer Vision,
Optimization, Inverse Problems, Wavelet analysis, etc.

We have no teaching tasks and check in / check out policy for
Postdoctoral Researchers.

- Prof. Jian Lu (Shenzhen Key Laboratory of Advanced Machine Learning
and Applications, Shenzhen University)
- Prof. Charles Chui (Editors-in-Chief of ACHA)

The salary is about 380,000 RMB (55,000 US dollars) per year. Those
who are interested please send their C.V. to Prof. Dr. Jian Lu,

From: Jan Giesselmann
Date: June 07, 2019
Subject: PhD or PostDoc Position, Hyperbolic Conservation Laws, TU Darmstadt

Applications are invited for a three year position within the
Numerical Analysis and Scientific Computing Group at Technische
Universitaet Darmstadt, Germany.

The position includes research and teaching responsibilities (mostly
in German). It is open to MSc graduates wishing to study for a PhD and
PhD graduates wishing to undertake postdoctoral research. The
successful candidate will conduct fundamental research in analysis and
numerical methods for hyperbolic partial differential equations under
the guidance of Prof. Jan Giesselmann.

Applicants are asked to outline the connection of their research
interests to those of Jan Giesselmann in their application. Any
inquiries concerning potential research topics can be addressed to Jan
Giesselmann (

The highly motivated candidate should hold an MSc degree in
mathematics or a closely related subject and have a background in
analysis of or numerical methods for PDEs. Good programming skills
(MATLAB , Python, C or C++) are beneficial.

The position is for a fixed term of three years with the possibility
of extension. The preferred starting date is October 1, 2019. Salary
will be paid in accordance with the German TVL, salary group E13

This is part of a wider call for applications at the mathematics
department of Technische Universitaet Darmstadt which can be found

Please also see that source for details on the the application

From: Carina Bringedal
Date: June 04, 2019
Subject: PhD Position, Upscaling of Evaporation in Porous Media

The DFG-funded Collaborative Research Center "Interface-Driven Multi-
Field Processes in Porous Media - Flow, Transport and Deformation"
(SFB 1313) at the University of Stuttgart invites applications for one
full-time doctoral position for 2.5 years (with possibility of
extension). The selected candidate will be employed as research
assistant (TV-L 13).

The position is within the project "Pore scale formulations for
evaporation, and upscaling to REV-scale" (A05). The goal of this
project is to provide a better mathematical description of REV-scale
evaporation by starting with a pore-scale description of the relevant
processes and using upscaling to derive an effective model at REV
scale. The effect of the evolving liquid- gas interface will be
explicitly taken into account and different approaches to describe the
evolving interface at the pore scale will be investigated.

Applicants should hold a master's or equivalent degree in applied
mathematics or related discipline with above-average
results. Experience with asymptotic analysis and/or thermodynamic
modeling is a plus.

Application deadline: 28.06.
Starting date: As soon as possible.

For more information:

Applications with CV and transcript of records from bachelor and
master degree can be sent directly to

From: Dimitri Breda
Date: June 06, 2019
Subject: PhD Positions, Univ of Udine

Ph.D. Course in Computer Science, Mathematics and Physics, University
of Udine.

The call for admission 2019/20 is now open, applications are invited
for 10+2 positions.

All information can be found at

The deadline is July 10, 2019 at 02.00 p.m. (Italian time).

From: Badih Ghusayni
Date: June 03, 2019
Subject: Contents, Intl J Mathematics and Computer Science, 14 (3)

Contents, Vol. 14, no, 3, International Journal of Mathematics and
Computer Science (These papers can be downloaded freely via

1) Warud Nakkhasen, On Q-Fuzzy Hyperideals of Semihyperrings.

2) Faisal Al-kasasbeh, Subclass of Meromorphic bi-univalent functions.

3) Sasikan Pankaew, Amornrat Rattana, Ronnason Chinram, On the number
of monogenic subsemigroups of semigroups Zn.

4) Devendra Kumar, Manisha Vijayran, Generalized Orders and
Approximation Errors of Entire Harmonic Functions in Rn.

5) Rabha W. Ibrahim, Maslina Darus, Subordination inequalities of a
new Salagean-difference operator.

6) Alessandro Cotronei, A Characterization of Eisenstein Triples.

7) George Olufemi, Adeniran Olusola, Olaleru Johnson, LWPC

8) B. Elavarasan, K. Porselvi, Y. B. Jun, Hybrid generalized bi-ideals
in Semigroups.

9) Ayinla Ally Yeketi, Wan Ainun Mior Othman, A Compartmental Model on
the Effect of Quarantine on MDR-TB.

10) Suleyman Ediz, A note on angular geometric graphs.

11) Emad Az-Zo'bi, Peakon and Solitary Wave Solutions for The Modified
Fornberg-Whitham Equation using Simplest Equation Method.

12) Polatip Poungsumpao, Waraphorn Kaijae, Saranya Arayarangsi,

13) Aiyared Iampan, Fuzzy UP-ideals and fuzzy UP-subalgebras of UP-
algebras in term of level subsets.

14) Hassen Aydi, Arsalan Hojat Ansari, Bahman Moeini, Mohd Salmi Md
Noorani, Haitham Qawaqneh, Property Q on G-metric spaces via C-class

15) Aminu Barde, Normah Maan, Efficient Analytical Approach for
Nonlinear System of Delay Differential Equations.

16) Prapart Pue-on, Solving a System of MPEs by Modified Power Series

17) Ronnason Chinram, Winita Yonthanthum, On the regularity-
preserving elements in regular ordered semigroups.

18) M. M. El-Dessoky, Saeed Islam, Chirped Solitons in Generalized
Resonant Dispersive Nonlinear Schrodinger's equation.

19) Kateryna Nesvit, Michael Hoft, Klaus Schunemann, Prediction
algorithm of the receiving antenna location for quasi-optical circuit

From: Raimondas Ciegis
Date: June 07, 2019
Subject: Contents, Mathematical Modeling and Analysis, 24 (3)


The Baltic Journal on Mathematical Applications, Numerical Analysis
and Differential Equations
ISSN 1392-6292, ISSN 1648-3510 online, Electronical edition:

Raimondas {\v{C}}iegis (Editor) Volume 24, Issue 3, 2019 (p.311-478)


Khosro Sayevand, Mittag-Leffler String Stability of Singularly
Perturbed Stochastic Systems within Local Fractal Space

Alicia Cordero, Juan R. Torregrosa and Pura Vindel, Dynamical Analysis
to Explain the Numerical Anomalies in the Family of Ermakov-Kalitkin
Type Methods

Lamia Chouchane and Lynda Selmani, A History-Dependent Frictional
Contact Problem with Wear for Thermoviscoelastic Materials

Klaus R. Schneider, The Point Charge Oscillator: Qualitative and
Analytical Investigations

Srikumar Acharya, Berhanu Belay and Rajashree Mishra, Multi-Objective
Probabilistic Fractional Programming Problem Involving Two Parameters
Cauchy Distribution

Lahoucine Elaissaoui and Zine El-Abidine Guennoun, Log-Tangent
Integrals and the Riemann Zeta Function

Ramandeep Behl, Vinay Kanwar and Young Ik Kim, Higher-Order Families
of Multiple Root Finding Methods Suitable for Non-Convergent Cases and
their Dynamics

Sanaz Pourrazi, Farshid Khojasteh, Mojgan Javahernia and Hassan
Khandani, An Affirmative Answer to Quasi-Contractions' Open Problem
under Some Local Constraints in $\mathbf{JS}-$metric Spaces

Sagar T. Sutar and Kishor D. Kucche, On Fractional Volterra
Integrodifferential Equations with Fractional Integrable Impulses

End of Digest