The Gromov–Lawson–Chernysh surgery theorem

This is an expository article without any claim of originality. We give a complete and self-contained account of the Gromov–Lawson–Chernysh surgery theorem for positive scalar curvature metrics.

An Education of Intuition and Process: Learning Architectural Design at Hong Kong Design Institute

This paper is a positioning statement and expository article describing design and fabrication projects built by students and faculty of the Hong Kong Design Institute’s (HKDI’s) Architecture programme. Through a series of experimental design-build projects, HKDI faculty teaches students the knowledge and experience to be gained through personal fabrication work, whether wholly manual or digitally assisted. The author stages the work against a series of excerpts from notable architects’ writings, describing a field of study relating tacit knowledge, architectural education, and fabrication specifics students explore through projects in Hong Kong and South China. Lessons and summary bodies of knowledge drawn from these preliminary projects define the path forward for HKDI’s spatial design pedagogy and research.

A Study on Domination in two Fuzzy Models

The aim of this 9th expository article is to conclude a study on domination in two fuzzy models, including t−norm fuzzy graphs and fuzzy graphs. All parts are twofold even if we don’t men- tion, directly. I.e., all results depicts some properties about fuzzy graph and t−norm fuzzy graph.

The sword-violence of Luke’s gospel: An overview of text segments

Though most readers of the Gospel of Luke are familiar with Jesus’s well-known statement about “taking up a sword” (Luke 22:49), Gospel also references other sword-violence text segments. The first reference occurs at Jesus’s birth (Luke 2:34, 35), and the last ends with Jesus’s arrest (Luke 22:47–53). This expository article focuses upon reading Luke’s sword-violence passages with a wholistic lens that includes the theological, cultural, and social cues within the text. In this integrated reading approach, one captures the Lukan depiction of various dimensions of violence via a sword and the implicit and explicit challenge to resist sword-violence as the way for followers of Jesus.

On Reliability of the COVID-19 Forecasts

In this expository article, we are aiming to show with an example that even short term forecasts regarding the COVID-19 spread pattern may sometimes not be very reliable. We have studied data published by Worldometers.info to get numerically an approximate formula of the spread pattern for a short period. We have observed that in the United States of America, there was a nearly exponential spread pattern for a very short period from May 3 to May 8, 2020. From May 9 to May 13, the nearly exponential character of the spread was found to be absent. Hence it can be concluded that the COVID-19 spread pattern, even after more than four months from the start of the outbreak, is not quite predictable. Therefore even short term forecasts regarding the spread may not be very reliable. We have found that forecasts using the assumption of an exponential pattern of spread may actually lead to overestimation.

On the Sign of the Curvature of a Contact Metric Manifold

In this expository article, we discuss the author’s conjecture that an associated metric for a given contact form on a contact manifold of dimension ≥5 must have some positive curvature. In dimension 3, the standard contact structure on the 3-torus admits a flat associated metric; we also discuss a local example, due to Krouglov, where there exists a neighborhood of negative curvature on a particular 3-dimensional contact metric manifold. In the last section, we review some results on contact metric manifolds with negative sectional curvature for sections containing the Reeb vector field.

Nikfar Domination Versus Others: Restriction, Extension Theorems and Monstrous Examples

The aim of this expository article is to present recent developments in the centuries-old discussion on the interrelations between several types of domination in graphs. However, the novelty even more prominent in the newly discovered simplified presentations of several older results. Domination can be seen as arising from real-world application and extracting classical results as first described by this article.The main part of this article, concerning a new domination and older one, is presented in a narrative that answers two classical questions: (i) To what extend must closing set be dominating? (ii) How strong is the assumption of domination of a closing set? In a addition, we give an overview of the results concerning domination. The problem asks how small can a subset of vertices be and contain no edges or, more generally how can small a subset of vertices be and contain other ones. Our work was as elegant as it was unexpected being a departure from the tried and true methods of this theory that had dominated the field for one fifth a century. This expository article covers all previous definitions. The inability of previous definitions in solving even one case of real-world problems due to the lack of simultaneous attentions to the worthy both of vertices and edges causing us to make the new one. The concept of domination in a variety of graphs models such as crisp, weighted and fuzzy, has been in a spotlight. We turn our attention to sets of vertices in a fuzzy graph that are so close to all vertices, in a variety of ways, and study minimum such sets and their cardinality. A natural way to introduce and motivate our subject is to view it as a real-world problem. In its most elementary form, we consider the problem of reducing waste of time in transport planning. Our goal here is to first describe the previous definitions and the results, and then to provide an overview of the flows ideas in their articles. The final outcome of this article is twofold: (i) Solving the problem of reducing waste of time in transport planning at static state; (ii) Solving and having a gentle discussions on problem of reducing waste of time in transport planning at dynamic state. Finally, we discuss the results concerning holding domination that are independent of fuzzy graphs. We close with a list of currently open problems related to this subject. Most of our exposition assumes only familiarity with basic linear algebra, polynomials, fuzzy graph theory and graph theory.

Nikfar Domination in Fuzzy Graphs

The aim of this expository article is to present recent developments in the centuries-old discussion on the interrelations between several types of domination in graphs. However, the novelty even more prominent in the newly discovered simplified presentations of several older results. The main part of this article, concerning a new domination and older one, is presented in a narrative that answers two classical questions: (i) To what extend must closing set be dominating? (ii) How strong is the assumption of domination of a closing set? In a addition, we give an overview of the results concerning domination. The problem asks how small can a subset of vertices be and contain no edges or, more generally how can small a subset of vertices be and contain other ones. Our work was as elegant as it was unexpected being a departure from the tried and true methods of this theory that had dominated the field for one fifth a century. This expository article covers all previous definitions. The inability of previous definitions in solving even one case of real-world problems due to the lack of simultaneous attentions to the worthy both of vertices and edges causing us to make the new one. The concept of domination in a variety of graphs models such as crisp, weighted and fuzzy, has been in a spotlight. We turn our attention to sets of vertices in a fuzzy graph that are so close to all vertices, in a variety of ways, and study minimum such sets and their cardinality. A natural way to introduce and motivate our subject is to view it as a real-world problem. In its most elementary form, we consider the problem of reducing waste of time in transport planning. Our goal here is to first describe the previous definitions and the results, and then to provide an overview of the flows ideas in their articles. The final outcome of this article is twofold: (i) Solving the problem of reducing waste of time in transport planning at static state; (ii) Solving and having a gentle discussions on problem of reducing waste of time in transport planning at dynamic state. Finally, we discuss the results concerning holding domination that are independent of fuzzy graphs. We close with a list of currently open problems related to this subject. Most of our exposition assumes only familiarity with basic linear algebra, polynomials, fuzzy graph theory and graph theory.

The Zeta and Related Functions: Recent Developments

The main object of this survey-cum-expository article is to present an overview of some recent developments involving the Riemann Zeta function ζ(s), the Hurwitz (or generalized) Zeta function ζ(s, a), and the Hurwitz-Lerch Zeta function Φ(z, s, a), which have their roots in the works of the great eighteenth-century Swiss mathematician, Leonhard Euler (1707–1783) and the Russian mathematician, Christian Goldbach (1690–1764). We aim at considering the problems associated with the evaluations and representations of ζ(s) when s ∈ N \ {1}, N is the set of natural numbers, with emphasis upon several interesting classes of rapidly convergent series representations for ζ(2n+1) (n ∈ N). Symbolic and numerical computations using Mathematica (Version 4.0) for Linux will also be provided for supporting their computational usefulness. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Jesus and the challenging gift of the other: An expository article on Mark 7:24–30

Mark 7:24–30 tells the story of Jesus’ surprising encounter and sharp verbal exchange with a Syrophoenician woman who sought healing for her demon-oppressed daughter. The woman embodies otherness in many dimensions: religious, ethnic, status, and gender. Jesus’ initial response to her request, expressed in a harsh-sounding parabolic proverb, is resistance and reluctance. This article explores possible reasons for that reluctance and suggests that Jesus initially understood that the Reign of God would be realized first among Jews and only later among Gentiles. The woman’s clever response to Jesus, as well as her insistence on the inclusiveness of divine mercy, served to change Jesus’ mind about the order and timing of the fulfillment of God’s in-breaking rule and reign. This article takes the view that Jesus’ change of mind can serve as a model for contemporary followers of Jesus who sometimes struggle to receive the challenging gifts of otherness. It also affirms that “the others” often have both insights and courage which may be catalytic for the growth of those who encounter them.