Linking Number of Singular Links and the Seifert Matrix

2007 ◽  
Vol 50 (3) ◽  
pp. 390-398 ◽  
Author(s):  
James J. Hebda ◽  
Chun-Chung Hsieh ◽  
Chichen M. Tsau

AbstractWe extend the notion of linking number of an ordinary link of two components to that of a singular link with transverse intersections, in which case the linking number is a half-integer. We then apply it to simplify the construction of the Seifert matrix, and therefore the Alexander polynomial, in a natural way.

1983 ◽  
Vol 35 (2) ◽  
pp. 311-323
Author(s):  
Quach Thi Cam Van

The notion of a prime tangle is introduced by Kirby and Lickorish [7]. It is related deeply to the notion of a prime knot by the following result in [8]: summing together two prime tangles gives always a prime knot.The purpose of this paper is to exploit this above mentioned result of Lickorish in creating or detecting prime knots which satisfy certain properties. First, we shall express certain knots (two-bridge knots and Terasaka slice knots [14]) as a sum of a prime tangle and an untangle (the existence of such a sum is proven to every knot in [7] and is not unique) in a natural way (natural means here depending on certain specific geometrical characters of the class of knots). Second, every Alexander polynomial (or Conway polynomial) is shown to be realized by a prime algebraic knot (algebraic in the sense of Conway [3], Bonahon-Siebenmann [2]) which can be expressed as the sum of two prime algebraic tangles.


Author(s):  
Nikolay S. Savkin

Introduction. Radical pessimism and militant anti-natalism of Arthur Schopenhauer and David Benathar create an optimistic philosophy of life, according to which life is not meaningless. It is given by nature in a natural way, and a person lives, studies, works, makes a career, achieves results, grows, develops. Being an active subject of his own social relations, a person does not refuse to continue the race, no matter what difficulties, misfortunes and sufferings would be experienced. Benathar convinces that all life is continuous suffering, and existence is constant dying. Therefore, it is better not to be born. Materials and Methods. As the main theoretical and methodological direction of research, the dialectical materialist and integrative approaches are used, the realization of which, in conjunction with the synergetic technique, provides a certain result: is convinced that the idea of anti-natalism is inadequate, the idea of giving up life. A systematic approach and a comprehensive assessment of the studied processes provide for the disclosure of the contradictory nature of anti-natalism. Results of the study are presented in the form of conclusions that human life is naturally given by nature itself. Instincts, needs, interests embodied in a person, stimulate to active actions, and he lives. But even if we finish off with all of humanity by agreement, then over time, according to the laws of nature and according to evolutionary theory, man will inevitably, objectively, and naturally reappear. Discussion and Conclusion. The expected effect of the idea of inevitability of rebirth can be the formation of an optimistic orientation of a significant part of the youth, the idea of continuing life and building happiness, development. As a social being, man is universal, and the awareness of this universality allows one to understand one’s purpose – continuous versatile development.


Author(s):  
Elizabeth Schechter

This chapter addresses the intuitive fascination of the split-brain phenomenon. According to what I call the standard explanation, it is because we ordinarily assume that people are psychologically unified, while split-brain subjects are not psychologically unified, which suggests that we might not be unified either. I offer a different interpretation. One natural way of grappling with people’s failures to conform to various assumptions we make about them is to conceptualize them as having multiple minds. Such multiple-minds models take their most dramatic form in narrative art as duality myths. The split-brain cases grip people in part because the subjects strike them as living embodiments of such myths.


Author(s):  
Stephen Piddock ◽  
Ashley Montanaro

AbstractA family of quantum Hamiltonians is said to be universal if any other finite-dimensional Hamiltonian can be approximately encoded within the low-energy space of a Hamiltonian from that family. If the encoding is efficient, universal families of Hamiltonians can be used as universal analogue quantum simulators and universal quantum computers, and the problem of approximately determining the ground-state energy of a Hamiltonian from a universal family is QMA-complete. One natural way to categorise Hamiltonians into families is in terms of the interactions they are built from. Here we prove universality of some important classes of interactions on qudits (d-level systems): We completely characterise the k-qudit interactions which are universal, if augmented with arbitrary Hermitian 1-local terms. We find that, for all $$k \geqslant 2$$ k ⩾ 2 and all local dimensions $$d \geqslant 2$$ d ⩾ 2 , almost all such interactions are universal aside from a simple stoquastic class. We prove universality of generalisations of the Heisenberg model that are ubiquitous in condensed-matter physics, even if free 1-local terms are not provided. We show that the SU(d) and SU(2) Heisenberg interactions are universal for all local dimensions $$d \geqslant 2$$ d ⩾ 2 (spin $$\geqslant 1/2$$ ⩾ 1 / 2 ), implying that a quantum variant of the Max-d-Cut problem is QMA-complete. We also show that for $$d=3$$ d = 3 all bilinear-biquadratic Heisenberg interactions are universal. One example is the general AKLT model. We prove universality of any interaction proportional to the projector onto a pure entangled state.


Chemistry ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 821-830
Author(s):  
Davide De Simeis ◽  
Stefano Serra ◽  
Alessandro Di Fonzo ◽  
Francesco Secundo

Natural flavor and fragrance market size is expected to grow steadily due to the rising consumer demand of natural ingredients. This market request is guided by the general opinion that the production of natural compounds leads to a reduction of pollution, with inherent advantages for the environment and people’s health. The biotransformation reactions have gained high relevance in the production of natural products. In this context, few pieces of research have described the role of microalgae in the oxidation of terpenoids. In this present study, we questioned the role of microalgal based oxidation in the synthesis of high-value flavors and fragrances. This study investigated the role of three different microalgae strains, Chlorella sp. (211.8b and 211.8p) and Chlorococcum sp. (JB3), in the oxidation of different terpenoid substrates: α-ionone, β-ionone, theaspirane and valencene. Unfortunately, the experimental data showed that the microalgal strains used are not responsible for the substrate oxidation. In fact, our experiments demonstrate that the transformation of the four starting compounds is a photochemical reaction that involves the oxygen as oxidant. Even though these findings cast a shadow on the use of these microorganisms for an industrial purpose, they open a new possible strategy to easily obtain nootkatone in a natural way by just using an aqueous medium, oxygen and light.


2021 ◽  
Vol 11 (4) ◽  
pp. 1616
Author(s):  
Antonina Rita Limongi ◽  
Emanuele Viviano ◽  
Maria De Luca ◽  
Rosa Paola Radice ◽  
Giuliana Bianco ◽  
...  

The need to safeguard our planet by reducing carbon dioxide emissions has led to a significant development of research in the field of alternative energy sources. Hydrogen has proved to be the most promising molecule, as a fuel, due to its low environmental impact. Even if various methods already exist for producing hydrogen, most of them are not sustainable. Thus, research focuses on the biological sector, studying microalgae, and other microorganisms’ ability to produce this precious molecule in a natural way. In this review, we provide a description of the biochemical and molecular processes for the production of biohydrogen and give a general overview of one of the most interesting technologies in which hydrogen finds application for electricity production: fuel cells.


2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Sicong Wang ◽  
Chen Wei ◽  
Yuanhua Feng ◽  
Hongkun Cao ◽  
Wenzhe Li ◽  
...  

AbstractAlthough photonics presents the fastest and most energy-efficient method of data transfer, magnetism still offers the cheapest and most natural way to store data. The ultrafast and energy-efficient optical control of magnetism is presently a missing technological link that prevents us from reaching the next evolution in information processing. The discovery of all-optical magnetization reversal in GdFeCo with the help of 100 fs laser pulses has further aroused intense interest in this compelling problem. Although the applicability of this approach to high-speed data processing depends vitally on the maximum repetition rate of the switching, the latter remains virtually unknown. Here we experimentally unveil the ultimate frequency of repetitive all-optical magnetization reversal through time-resolved studies of the dual-shot magnetization dynamics in Gd27Fe63.87Co9.13. Varying the intensities of the shots and the shot-to-shot separation, we reveal the conditions for ultrafast writing and the fastest possible restoration of magnetic bits. It is shown that although magnetic writing launched by the first shot is completed after 100 ps, a reliable rewriting of the bit by the second shot requires separating the shots by at least 300 ps. Using two shots partially overlapping in space and minimally separated by 300 ps, we demonstrate an approach for GHz magnetic writing that can be scaled down to sizes below the diffraction limit.


2020 ◽  
Vol 30 (Supplement_5) ◽  
Author(s):  
K Pluta ◽  
Ł Balwicki

Abstract Research shows that over 80% of smokers start their habit under the age of 18. A few years ago young people undertook risky behaviors related to nicotine initiation mainly by smoking cigarettes. Today, next to traditional tobacco products, electronic cigarettes are becoming more and more popular. Due to the prevalence of new forms of nicotine addiction, modification of anti-tobacco prevention programs is required. The purpose of the research was exploration - learning the opinions and attitudes of young people towards e-cigarettes. The qualitative study was conducted using the FGI method (focus group interview). The meetings were modereted by specially trained psychologists. 48 students participated in the meetings of six focus groups, divided by gender and smoking status (smokers/non-smokers). The participants are young people aged 15-19, attending high schools in Warsaw, Kielce and Lublin. In conversations, young people emphasized the impact of e-cigarettes in smoking initiation - it usually occurs at the age of 12-14. E-cigarettes are perceived as cigarettes “for younger”, non-addictive, less serious, providing more entertainment. 'Cloud chasing' is particularly popular. They perform social functions - they are helpful in establishing relationships. Teenagers do not see the harmfulness of e-cigarettes. Participants mentioned their advantages over traditional tobacco products - they can be smoked everywhere and do not leave an unpleasant smell. Some of the respondents admit to the simultaneous use of electronic and traditional cigarettes. Moreover, many parents allow children to smoke electronic cigarettes. Vaping have become a natural way to relaxation and socialization for adolescents. E-cigarettes do not have such a negative connotation as traditional tobacco products. Young people do not see them as harmful, which is a challenge for effective preventive measures. Key messages Adolescents do not see e-cigarettes as harmful, which is a challenge for effective preventive measures. Vaping have become more and more popular - it's natural way to relaxation and socialization for young people.


Sign in / Sign up

Export Citation Format

Share Document