Search

The profiles of the edge of rectangular sheets of paper folded so as to join opposite edges were measured and compared with the profiles calculated with the theory of elasticity. I show how the calculation can be accomplished by using the aspect ratio of the loops as the only input parameter. [ABSTRACT FROM AUTHOR]

Purpose: Part building orientation (PBO) is an important factor affecting the quality of laser powder bed fusion (L-PBF), which can affect the surface quality and manufacturing cost. The purpose of this paper is to propose a PBO optimization method to optimize the surface roughness and molding time of parts at the same time on the premise of small calculation scale and arbitrary resolution. Design/methodology/approach: Efficient and accurate evaluation is an important index of PBO optimization method. In this paper, a PBO optimization method based on scaling enumeration method is proposed, and the surface roughness and molding time of L-PBF parts are modeled as the objective evaluation function of PBO optimization process. To realize multi-objective optimization, an expert system is established, and the fuzzy multiple-attribute group decision-making theory is used to provide weights for each objective evaluation function. Findings: Research shows that the scaling-enumeration method can optimize the surface roughness and molding time at the same time and get the best PBO. Compared with the traditional method, the surface roughness and molding time are reduced by 1.1% and 0.58%, respectively, and the operation scale of the scaling-enumeration method is reduced by 99% compared with the traditional method. PBO with arbitrary angular resolution can be achieved. Originality/value: This paper presents a new method to optimize the forming direction of L-PBF parts. This method has small operation scale and accurate results, so it is meaningful for industrial application. [ABSTRACT FROM AUTHOR]

We use Regev's double centralizer theorem from [7] to study invariants of matrices with group actions. This theory then has applications to trace identities and Poincaré series. [ABSTRACT FROM AUTHOR]

This is an introduction to Bret Tilson's paper "Modules". [ABSTRACT FROM AUTHOR]

Abstract: This appendix collects some material on the cohomology of discrete subgroups of Lie groups and the theory of their representation varieties to provide background for the results of Sin and Thompson (2010, 2013) in [22,23]. [Copyright &y& Elsevier]

Let E/F be a cyclic extension of number fields of degree ℓn, where ℓ is a prime. It is proved that the ℓ-rank of the class group of E is bounded by ℓn(t-1+rkℓClF), where t is the number of primes of F, including infinite primes, which ramify in E and ClF is the class group of F. This generalizes a result of G. Cornell which applies when n = 1 and ℓ is odd. A similar result is shown to hold when the Galois group is an abelian ℓ-group and the Hasse norm theorem is valid for E/F. [ABSTRACT FROM AUTHOR]

Let $p$ be a prime for which the congruence group $\Gamma_0(p)^*$ is of genus zero, and let $j_p^*$ be the corresponding Hauptmodul. Let $f$ be a nearly holomorphic modular form of weight 1/2 on $\Gamma_0(4p)$ which satisfies some congruence condition on its Fourier coefficients. We interpret $f$ as a vector valued modular form. Applying Borcherds lifting of vector valued modular forms we construct infinite products associated to $j_p^*$ and relate them to Zagier's trace formula for the singular values of $j_p^*$. [ABSTRACT FROM AUTHOR]

Let k be a field of characteristic 0, and let f : kn→kn be a polynomial map with components of the form fi=xi+hi, where the hi are monomials. If the Jacobian determinant of the map f is a nonzero constant, then f is a tame automorphism. If, in addition, each hi is either constant or of degree 2 or more, then f is linearly triangularizable. [Copyright &y& Elsevier]

It is shown that an approach earlier used by the author for classification of closed simply connected 6-manifolds (reduction to the problem of calculating certain bordism groups) can also be applied for easily obtaining the results by Barden (1965) on classification of closed simply connected 5-manifolds. Bibliography: 11 titles. [ABSTRACT FROM AUTHOR]

China is at a critical moment of transforming high-speed development to high-quality development, and it is significant to improve the efficiency of green technological innovation. In this paper, under the perspective of two-stage innovation value chain, we construct the evaluation index system of green technology innovation efficiency, adopt the super efficiency SBM model to measure the green technology innovation efficiency of China's high-tech industries, and based on the results obtained, we assume the fuzzy set qualitative comparative analysis method (fs-QCA) based on the group theory to explore the complex causal mechanism and grouping paths of the interaction between enterprises, government and market that affects the green technology innovation efficiency Mechanism and group path. The study results show that (1) enterprise, government, and market are not necessary conditions to influence the efficiency of green technological innovation, and even if a particular party plays a central role, it needs the assistance of other parties. (2) The improvement of green technological innovation efficiency requires the interaction of enterprises, government, and market, and even if any party does not have the core conditions, it can still produce high green technological innovation efficiency. (3) The path of the "innovative compensation" effect is identified, which indicates that enterprises will generate a high level of green innovation efficiency under sufficient investment brought about by the enterprise scale effect and matched with a good level of economic development. (4) The market economy-led pathway suggests that when the market economy is highly developed, firms do not need environmental regulation and government support to generate efficient levels of green technological innovation. [ABSTRACT FROM AUTHOR]

The symmetry adapted counting rule for mechanisms and states of self-stress in symmetric frameworks is presented in an accessible and intuitive manner with the aim of empowering engineers who design such structures. By simply counting nodes and bars, it is possible to detect states of self-stress and mechanisms beyond the standard Maxwell-Calladine count. This methodology is first introduced without the need to understand the underlying group theory before being applied to a range of example frameworks. Design problems focusing on gridshells are discussed – it is noted that placing bars on lines of mirror symmetry tend to increase the number of states of self-stress in a framework, which can be desirable. This paper reformulates common symmetric frameworks and introduces simple rules regarding how to obtain a greater number of states of self-stress. By allowing for the design of states of self-stress, the forces in the structure can be designed with greater control. [ABSTRACT FROM AUTHOR]

In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received very little attention. In this paper, we will consider the philosophical tensions that Steingart uncovers, and use them to argue that the best account of the epistemic status of the Classification Theorem will be essentially and ineliminably social. This forms part of the broader argument that in order to understand mathematical proofs, we must appreciate their social aspects. [ABSTRACT FROM AUTHOR]

The article offers information on the journal, founded by Professor Bernhard Neumann. It mentions that the first issue of the journal appeared in August 1969; and also mentions the views of Neumann, that Mathematicians nowadays consider a publication delay well in excess of a year as inevitable and normal.

This study examines the exclusion of Vanessa Nakate, a Ugandan climate activist, from a group photo published by the Associated Press (AP) during the 2020 World Economic Forum. Using the muted group theory, it explores the implications of Nakate's omission as the sole Black individual in the image, shedding light on the broader issue of symbolic annihilation faced by Black women activists in Western media. Through visual and textual analysis, the study reveals the power dynamics and biases behind AP's decision to crop Nakate, fueling subsequent controversy. Furthermore, the paper examines AP's response to the backlash, analyzing their strategies to rebuild their reputation, including issuing an apology and releasing the original photograph. Plain language summary: Erasure of Black women activists from media: A review This paper looks at a photo from the 2020 World Economic Forum where a Ugandan climate activist named Vanessa Nakate was cropped out. The paper uses "muted group theory" to explain how this might have happened and what it means. It argues that Nakate was left out because she's a Black woman and that this is part of a bigger problem where the media often ignores or overlooks Black women activists. The focus is on the broader issue of symbolic annihilation experienced by Black women activists in Western media. Using visual and textual analysis, the study uncovers the power dynamics and biases influencing AP's decision to crop Nakate, sparking subsequent controversy. Additionally, the paper scrutinizes AP's response to the criticism, examining their strategies to rebuild their reputation, which include issuing an apology and releasing the original photograph. Overall, the paper is about how powerful media organizations can be and how important it is to be aware of the biases they might have. It is also about the importance of giving Black women activists a voice and making sure their stories are heard. [ABSTRACT FROM AUTHOR]

This paper is aimed at using a lookup table method to improve the scalar multiplication performance of elliptic curve cryptography. The lookup table must be divided into two polynomials and requires two iterations of point doubling operation, for which negation operations are needed. It is well known that an inversion operation requires a lot of multiplication time. The advantage of this paper is that we are able to reduce one inverse element calculation for this problem and also improve the basic operations of finite fields through segmentation methods. If the normal basis method is used in the design of the inverse element operation, it must be converted to the normal basis through the standard basis. However, the conversion process requires a lot of matrix operations. Though the anti-element operation has good speed performance, it also increases the computational complexity. Using number theory and grouping methods will greatly improve the performance of inverse element operations. With application of the two-time point doubling operation in the hardware implementation, the developed approach reduces the computing time by 48% as compared with the conventional approach. The computational time of the scalar multiplication using the presented method is further improved by 67% over the traditional algorithm with only an area increase of 12%. Finally, the proposed lookup table-based technique can be utilized for software and hardware implementation, as the developed arithmetic operations are simple and are consistent in their execution. [ABSTRACT FROM AUTHOR]

The aim of this research paper is to propose a framework to model, simulate and control the motion of a small spacecraft in the proximity of a space station. In particular, rendezvous in the presence of physical obstacles is tackled by a virtual potential theory within a modern manifold calculus setting and simulated numerically. The roto-translational motion of a spacecraft as well as the control fields are entirely formulated through a coordinate-free Lie group-type formalism. Likewise, the proposed control strategies are expressed in a coordinate-free setting through structured control fields. Several numerical simulations guide the reader through an evaluation of the most convenient control strategy among those devised in the present work. [ABSTRACT FROM AUTHOR]

This review paper gives an overview of the method of multipliers for partial differential equations (PDEs). This method has made possible a lot of solutions to PDEs that are of interest in many areas such as applied mathematics, mathematical physics, engineering, etc. Looking at the history of the method and synthesizing the newest developments, we hope to give it the attention that it deserves to help develop the vast amount of work still needed to understand it and make the best use of it. It is also an interesting and a relevant method in itself that could possibly give interesting results in areas of mathematics such as modern algebra, group theory, topology, etc. The paper will be structured in such a manner that the last review known for this method will be presented to understand the theoretical framework of the method and then later work done will be presented. The information of four recent papers further developing the method will be synthesized and presented in such a manner that anyone interested in learning this method will have the most relevant information available and have all details cited for checking. [ABSTRACT FROM AUTHOR]

Even in the highest-level mathematics courses at undergraduate institutions, most students do not read mathematical research from professional journals. Such depth of content is often reserved for “independent studies” or summer REU's. In this article I describe a course that required students to read research papers, all of which centered on a single theme. The course covered advanced group theory topics while conveying the notion that there is a mathematical community that works together to advance mathematical knowledge. Using a single story as an integrative thread is an approach that can be adapted to any topic in mathematics. [ABSTRACT FROM AUTHOR]

To what extent can hostility toward Greeks in Turkish politics be explained sociologically? This paper provides a fresh perspective by examining the value of group position theory in understanding negative perceptions of Greeks in Turkish politics between 1946 and 1960. It proposes that Turkish politicians' perceived threats to valued resources played a key role in their unfavorable portrayals of Greeks. To test the argument, the study scrutinizes all Turkish parliamentary speeches in this period that contain the word Greek (N = 652). Quantitative analysis demonstrates that speaking about border-related threats is a significant predictor of negative perceptions. Qualitative investigation details how politicians justified their negative comments. The paper concludes that the negative remarks about Greeks are a function of Turkish politicians' perceived threats to valued resources. [ABSTRACT FROM AUTHOR]

Presenting sporadic simple groups as an automorphism groups of designs and graphs is an exciting field in finite group theory. In this paper, with two different methods, we present some new resolvable simple 3-designs with Higman-Sims sporadic simple group HS as the full automorphism group. Also, we classify all block-transitive self-orthogonal designs on 176 points with even block size that admit sporadic simple group HS as an automorphism group. Furthermore, with these methods we construct some new resolvable 3-designs on 36, 40, 120 and 176 points. [ABSTRACT FROM AUTHOR]

Coordination sequences (also called growth functions) appear in various areas of chemistry and crystallography, such as ice crystals and zeolites, and various areas of mathematics, such as lattice theory and geometric group theory. Cannon's method of cone types is modified for finding the coordination sequence of the Cayley graph of a group. This method is then applied to compute the growth functions and the growth series of the Cayley graphs of the wallpaper groups (the 2D crystallographic groups). The paper has several tables and colored figures summarizing and illustrating the results. [ABSTRACT FROM AUTHOR]

This paper explores the development of two theories of human behavior as they relate to work systems. Both Murray Bowen and Barry Oshry formulated theories of how people operate in groups. Bowen developed his theory through observation of families and extended his thinking to apply more broadly. Oshry observed work systems in his lab and thought what he saw there could also be true in families and society at large. Practitioners have applied both theories in their work with groups. However, neither theory has received much attention in terms of the theoretical concepts they contain or the processes the theoreticians used to generate them. The purpose of this paper is to examine the methods these two theorists use to create their frameworks, compare and contrast the theories they posited as a result, and consider the possible future development for them. [ABSTRACT FROM AUTHOR]

Indigenous groups voices have often been missing from the marketing research collegiate. The Aboriginal and Torres Strait Islander Peoples of the land now known as Australia, for example, are among the most researched peoples in the world (Martin & Mirraboopa, 2003), yet are underrepresented among research practitioners. The present underrepresentation among practitioners is only slowly, and occasionally haphazardly, being addressed by the growing number of more junior Indigenous researchers entering the field. Until greater representation among senior researchers is achieved, research teams are likely to include a mixture of Indigenous and non-Indigenous researchers. Such teams must therefore address a unique combination of power imbalance and minority inclusion in how they work. This need for inclusion can become more challenging for research teams when the research topic addresses issues impacting Indigenous peoples. And while numerous ethical and research guidelines exist for how researchers work with participants who are members of a minority group and are likely to have less power, there are few frameworks addressing how such challenges should be managed for the researchers within a research team. In this paper, we use an action research method to critically reflect on how to manage research teams that include more junior Indigenous researchers whose voices are vital to the research project. Reflexive and proactive processes were developed to ensure a culture of reflection both regarding interactions within the research team and in the project. To structure and share these reflections, the team developed and enunciated a fit-for-purpose framework. This framework was informed by the work of Narungga Professor Rigney (1999) that lists foundational Indigenist research methods. The framework also draws on the layers of reflexivity proposed by Nicholls (2009) and insider/outsider group theory previously advocated for (Ameka, 2018). [ABSTRACT FROM AUTHOR]

Clinical curative effect is the core value and fundamental pursuit of medicine. The data-driven clinical quantitative evaluation model is an important research issue in clinical efficacy evaluation. The existing clinical efficacy evaluation methods have made a lot of contributions to the structured information of static attributes, but less attention is paid to the heterogeneous information with dynamic and random characteristics. This paper discusses a class of clinical efficacy evaluation decision-making problems that contain both time-series and dynamic characteristics and uses the three-way decision principle to describe these characteristics. The group decision-making theory is introduced to aggregate the evaluation information of time series dynamic features generated in the decision-making process. A time series dynamic three-way group decision model for clinical efficacy evaluation is constructed, the optimal decision rules with minimum expected loss objective are calculated and proofed in the proposed model, and then the optimal treatment alternative is obtained. Finally, taking the decision-making problem of clinical efficacy evaluation of traditional Chinese medicine (TCM) treatment of atopic dermatitis as the research object, based on the actual clinical data of Guangdong Provincial Hospital of TCM, the decision-making process and steps of the theoretical model constructed in this paper are verified and applied. The data-driven quantitative clinical evaluation model has achieved better application effects than the actual clinical scenarios. The research results in this paper provide new ideas and theoretical methods for real-world clinical efficacy evaluation research. [ABSTRACT FROM AUTHOR]

In this paper, the A -theory, an extension of F-theory, is described as a fully U-duality covariant brane theory. This theory has some distinguishing features not known from world-sheet models. In particular, seen as a sigma model, both world-volume and target space coordinates are specific representations of the same group (the U-duality group). The U-duality group in question is an exceptional group (a split form of the Ed series). The structure of this group allows it to encompass both the T-duality group of string theory as well as the general linear symmetry group of M -theory. A -theory is defined by the current algebras in Hamiltonian formalism, or by world-volume actions in Lagrangian formalism. The spacetime coordinates are selfdual gauge fields on the world-volume, requiring the Gauß law constraints tying the world-volume to spacetime. Solving the Gauß law constraints/the Virasoro constraints gives the world-volume/spacetime sectioning from A -theory to T -theory/ M -theory respectively. The A -theory Lagrangian admits extended symmetry which has not been observed previously in the literature, where the background fields include both the spacetime and the world-volume gravitational fields. We also constructed the four-point amplitude of A -theory in the low energy limit. The amplitude is written in a way that the U-duality symmetry is manifest, but after solving the section condition, it reduces to the usual four-graviton amplitude. In the previous papers, we have referred to this model as F-theory, however, F-theory initiated by Vafa is now a big branch of string theory as the study of elliptic fibrations, so we refer to these constructions as generalized models of theory for all dimensions with all duality symmetries as A -theory. [ABSTRACT FROM AUTHOR]