Search results for: Goldbach conjecture

Authors: Yingxu Wang

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The base 6 structure and properties of mirror primes are discovered in this work towards the proof of Goldbach Conjecture. This paper reveals a fundamental pattern on pairs of mirror primes adjacent to any even number nₑ > 2 with symmetrical distances on both sides determined by a methodology of Mirror Prime Decomposition (MPD). MPD leads to a formal proof of the Goldbach conjecture, which states that the conjecture holds because any pivot even number, nₑ > 2, is a sum of at least an adjacent pair of primes divided by 2. This work has not only revealed the analytic pattern of base 6 primes but also proven the infinitive validation of the Goldbach conjecture.

Keywords: number theory, primes, mirror primes, double recursive patterns, Goldbach conjecture, formal proof, mirror-prime decomposition, applications

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Authors: Hashem Sazegar

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In 1937, Vinograd of Russian Mathematician proved that each odd large number can be shown by three primes. In 1973, Chen Jingrun proved that each odd number can be shown by one prime plus a number that has maximum two primes. In this article, we state one proof for Goldbach’conjecture. Introduction: Bertrand’s postulate state for every positive integer n, there is always at least one prime p, such that n < p < 2n. This was first proved by Chebyshev in 1850, which is why postulate is also called the Bertrand-Chebyshev theorem. Legendre’s conjecture states that there is a prime between n2 and (n+1)2 for every positive integer n, which is one of the four Landau’s problems. The rest of these four basic problems are; (i) Twin prime conjecture: There are infinitely many primes p such that p+2 is a prime. (ii) Goldbach’s conjecture: Every even integer n > 2 can be written asthe sum of two primes. (iii) Are there infinitely many primes p such that p−1 is a perfect square? Problems (i), (ii), and (iii) are open till date.

Keywords: Bertrand-Chebyshev theorem, Landau’s problems, twin prime, Legendre’s conjecture, Oppermann’s conjecture

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Authors: Hashem Sazegar

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Legendre’s conjecture states that there is a prime number between n^2 and (n + 1)^2 for every positive integer n. In this paper we prove that every composite number between n2 and (n + 1)2 can be written u^2 − v^2 or u^2 − v^2 + u − v that u > 0 and v ≥ 0. Using these result as well as induction and residues (modq) we prove Legendre’s conjecture.

Keywords: bertrand-chebyshev theorem, landau’s problems, goldbach’s conjecture, twin prime, ramanujan proof

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Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su

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In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.

Keywords: complement, degree sum, hamiltonian, tough

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Authors: Supratman Ahman Maedi

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The construction of knowledge is the goal of learning. The purpose of this research is to know how the role of Piaget theory in allegation via analogy reasoning. This study uses Think out loads when troubleshooting. To explore conjecturing via analogical reasoning is given the question of open analogy. The result: conjecture via analogical reasoning has been done by students in the construction of knowledge, in conjecture there are differences in thinking flow depending on the basic knowledge of the students, in the construction of knowledge occurs assimilation and accommodation problems, strategies and relationships.

Keywords: analogical reasoning, conjecturing, knowledge construction, Piaget's theory

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Authors: Yingxu Wang

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This work presents basic research on the recursive structures and dual sequential patterns of primes for the formal proof of the Twin-Prime Conjecture (TPC). A rigorous methodology of Twin-Prime Decomposition (TPD) is developed in MATLAB to inductively verify potential twins in the dual sequences of primes. The key finding of this basic study confirms that the dual sequences of twin primes are not only symmetric but also infinitive in the unique base 6 cycle, except a limited subset of potential pairs is eliminated by the lack of dual primality. Both theory and experiments have formally proven that the infinity of twin primes stated in TPC holds in the P x P space.

Keywords: number theory, primes, twin-prime conjecture, dual primes (P x P), twin prime decomposition, formal proof, algorithm

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Authors: Francisco Bulnes

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Through the Fukaya conjecture and the wrapped Floer cohomology, the correspondences between paths in a loop space and states of a wrapping space of states in a Hamiltonian space (the ramification of field in this case is the connection to the operator that goes from TM to T*M) are demonstrated where these last states are corresponding to bosonic extensions of a spectrum of the space-time or direct image of the functor Spec, on space-time. This establishes a distinguished diffeomorphism defined by the mapping from the corresponding loops space to wrapping category of the Floer cohomology complex which furthermore relates in certain proportion D-branes (certain D-modules) with strings. This also gives to place to certain conjecture that establishes equivalences between moduli spaces that can be consigned in a moduli identity taking as space-time the Hitchin moduli space on G, whose dual can be expressed by a factor of a bosonic moduli spaces.

Keywords: Floer cohomology, Fukaya conjecture, Lagrangian submanifolds, quantum topological diffeomorphism

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Authors: Jiaqi Huang, Yuheng Wang

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Premises selection, the task of selecting a set of axioms for proving a given conjecture, is a major bottleneck in automated theorem proving. An array of deep-learning-based methods has been established for premises selection, but a perfect performance remains challenging. Our study examines the inaccuracy of deep neural networks in premises selection. Through training network models using encoded conjecture and axiom pairs from the Mizar Mathematical Library, two potential biases are found: the network models classify more premises as necessary than unnecessary, referred to as the ‘positive bias’, and the network models perform better in proving conjectures that paired with more axioms, referred to as ‘length bias’. The ‘positive bias’ and ‘length bias’ discovered could inform the limitation of existing deep neural networks.

Keywords: automated theorem proving, premises selection, deep learning, interpreting deep learning

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Authors: Elvira Kusniyanti, Hanni Garminia, Pudji Astuti

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This research studies an interconnection between finitely generated uniform modules and Dedekind prime rings. The characterization of modules over Dedekind prime rings that will be investigated is an adoption of Noetherian and hereditary concept. Dedekind prime rings are Noetherian and hereditary rings. This property of Dedekind prime rings is a background of the idea of adopting arises. In Noetherian area, it was known that a ring R is Noetherian ring if and only if every finitely generated R-module is a Noetherian module. Similar to that result, a characterization of the hereditary ring is related to its projective modules. That is, a ring R is hereditary ring if and only if every projective R-module is a hereditary module. Due to the above two results, we suppose that characterization of a Dedekind prime ring can be analyzed from finitely generated modules over it. We propose a conjecture: a ring R is a Dedekind prime ring if and only if every finitely generated uniform R-module is a Dedekind module. In this article, we will generalize a concept of the Dedekind module for non-commutative ring case and present a part of the above conjecture.

Keywords: dedekind domains, dedekind prime rings, dedekind modules, uniform modules

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Authors: David A. Harness

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Natural evolution of ATP cognitive systems is to meet AI peer review standards. ATP process of axiom selection from Mizar to prove a conjecture would be further refined, as in all human and machine learning, by solving the real world problem of the proposed AI peer review challenge: Determine which conjecture forms the higher confidence level constructive proof between Standard Model of Physics SU(n) lattice gauge group operation vs. present non-standard 4D GEM EOS SU(n) lattice gauge group spatially extended operation in which the photon and electron are the first two trace angular momentum invariants of a gravitoelectromagnetic (GEM) energy momentum density tensor wavetrain integration spin-stress pressure-volume equation of state (EOS), initiated via 32 lines of Mathematica code. Resulting gravitoelectromagnetic spectrum ranges from compressive through rarefactive of the central cosmological constant vacuum energy density in units of pascals. Said self-adjoint group operation exclusively operates on the stress energy momentum tensor of the Einstein field equations, introducing quantization directly on the 4D spacetime level, essentially reformulating the Yang-Mills virtual superpositioned particle compounded lattice gauge groups quantization of the vacuum—into a single hyper-complex multi-valued GEM U(1) × SU(1,3) lattice gauge group Planck spacetime mesh quantization of the vacuum. Thus the Mizar corpus already contains all of the axioms required for relevant DeepMath premise selection and unambiguous formal natural language parsing in context deep learning.

Keywords: automated theorem proving, constructive quantum field theory, information theory, neural networks

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Authors: Bin Sheng, Changhong Lu

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Let G be a simple undirected graph with no isolated vertex. A paired dominating set of G is a dominating set which induces a subgraph that has a perfect matching. The paired domination number of G, denoted by γₚᵣ(G), is the size of its smallest paired dominating set. Goddard and Henning conjectured that γₚᵣ(G) ≤ 4n/7 holds for every graph G with δ(G) ≥ 3, except the Petersen Graph. In this paper, we prove this conjecture for cubic graphs.

Keywords: paired dominating set, upper bound, cubic graphs, weight function

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Authors: Hamid Abchir, Mohammed Sabak2

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We construct an infinite family of links which are both almost alternating and quasi-alternating from a given either almost alternating diagram representing a quasi-alternating link, or connected and reduced alternating tangle diagram. To do that we use what we call a dealternator extension which consists in replacing the dealternator by a rational tangle extending it. We note that all non-alternating and quasi-alternating Montesinos links can be obtained in that way. We check that all the obtained quasi-alternating links satisfy Conjecture 3.1 of Qazaqzeh et al. (JKTR 22 (6), 2013), that is the crossing number of a quasi-alternating link is less than or equal to its determinant. We also prove that the converse of Theorem 3.3 of Qazaqzeh et al. (JKTR 24 (1), 2015) is false.

Keywords: quasi-alternating links, almost alternating links, tangles, determinants

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Authors: Shai Sarussi

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The union of a nonempty chain of prime ideals in a noncommutative ring is not necessarily a prime ideal. An ideal is called union-prime if it is a union of a nonempty chain of prime ideals but is not a prime. In this paper, some relations between chains of prime ideals and the induced chains of union-prime ideals are shown; in particular, the cardinality of such chains and the cardinality of the sets of cuts of such chains are discussed. For a ring R and a nonempty full chain of prime ideals C of R, several characterizations for the property of immediate neighbors in C are given.

Keywords: prime ideals, union-prime ideals, immediate neighbors, Kaplansky's conjecture

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Authors: Shin-Shin Kao, Hsiu-Chunj Pan

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Given a graph G. A cycle of G is a sequence of vertices of G such that the first and the last vertices are the same. A hamiltonian cycle of G is a cycle containing all vertices of G. The graph G is k-ordered (resp. k-ordered hamiltonian) if for any sequence of k distinct vertices of G, there exists a cycle (resp. hamiltonian cycle) in G containing these k vertices in the specified order. Obviously, any cycle in a graph is 1-ordered, 2-ordered and 3-ordered. Thus the study of any graph being k-ordered (resp. k-ordered hamiltonian) always starts with k = 4. Most studies about this topic work on graphs with no real applications. To our knowledge, the chordal ring families were the first one utilized as the underlying topology in interconnection networks and shown to be 4-ordered [1]. Furthermore, based on computer experimental results in [1], it was conjectured that some of them are 4-ordered hamiltonian. In this paper, we intend to give some possible directions in proving the conjecture.

Keywords: Hamiltonian cycle, 4-ordered, Chordal rings, 3-regular

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Authors: M. Abdelmalek

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In this work, we study the hypersurfaces of constant weighted mean curvature embedded in weighted manifolds. We give a condition about these hypersurfaces to be minimal. This condition is given by the ellipticity of the weighted Newton transformations. We especially prove that two compact hypersurfaces of constant weighted mean curvature embedded in space forms and with the intersection in at least a point of the boundary must be transverse. The method is based on the calculus of the matrix of the second fundamental form in a boundary point and then the matrix associated with the Newton transformations. By equality, we find the weighted elementary symmetric function on the boundary of the hypersurface. We give in the end some examples and applications. Especially in Euclidean space, we use the above result to prove the Alexandrov spherical caps conjecture for the weighted case.

Keywords: weighted mean curvature, weighted manifolds, ellipticity, Newton transformations

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Authors: T. Martini, J. M. Martínez

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An algorithmic acceleration strategy based on quasi-Newton (or secant) methods is displayed for address the practical problem of accelerating the convergence of the Newton-Lagrange method in the case of convergence to critical multipliers. Since the Newton-Lagrange iteration converges locally at a linear rate, it is natural to conjecture that quasi-Newton methods based on the so called secant equation and some minimal variation principle, could converge superlinearly, thus restoring the convergence properties of Newton's method. This strategy can also be applied to accelerate the convergence of algorithms applied to fixed-points problems. Computational experience is reported illustrating the efficiency of this strategy to solve fixed-point problems with linear convergence rate.

Keywords: algorithmic acceleration, fixed-point problems, nonlinear programming, quasi-newton method

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Authors: Valentina Zhang

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While facial expression is a complex and individualized behavior, all facial emotion recognition (FER) systems known to us rely on a single facial representation and are trained on universal data. We conjecture that: (i) different facial representations can provide different, sometimes complementing views of emotions; (ii) when employed collectively in a discussion group setting, they enable more accurate emotion reading which is highly desirable in autism care and other applications context sensitive to errors. In this paper, we first study FER using pixel-based DL vs semantics-based DL in the context of deepfake videos. Our experiment indicates that while the semantics-trained model performs better with articulated facial feature changes, the pixel-trained model outperforms on subtle or rare facial expressions. Armed with these findings, we have constructed an adaptive FER system learning from both types of models for dyadic or small interacting groups and further leveraging the synthesized group emotions as the ground truth for individualized FER training. Using a collection of group conversation videos, we demonstrate that FER accuracy and personalization can benefit from such an approach.

Keywords: neurodivergence care, facial emotion recognition, deep learning, ground truth for supervised learning

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Authors: Wongsakorn Charoenpanitseri

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The total chromatic number χ"(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no incident or adjacent pair of elements receive the same color Let G be a graph with maximum degree Δ(G). Considering a total coloring of G and focusing on a vertex with maximum degree. A vertex with maximum degree needs a color and all Δ(G) edges incident to this vertex need more Δ(G) + 1 distinct colors. To color all vertices and all edges of G, it requires at least Δ(G) + 1 colors. That is, χ"(G) is at least Δ(G) + 1. However, no one can find a graph G with the total chromatic number which is greater than Δ(G) + 2. The Total Coloring Conjecture states that for every graph G, χ"(G) is at most Δ(G) + 2. In this paper, we prove that the Total Coloring Conjectur for a Δ-claw-free 3-degenerated graph. That is, we prove that the total chromatic number of every Δ-claw-free 3-degenerated graph is at most Δ(G) + 2.

Keywords: total colorings, the total chromatic number, 3-degenerated, CLAW-FREE

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Authors: EMMANUEL DWAMENA SASU

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International climate policy actions require countries under Paris Agreement to design instruments, provide support (financial and technical), and strengthen institutional capacity with tendency to transcending policy formulation to implementation and sustainability. Changes associated with moisture depletion has been a growing phenomenon; especially in developing countries with projected global GDP drop from 7% to 2% between 2005 and 2050. These developments have potential to adversely affect food production in feeding the growing world population, with corresponding rise in global hunger. Incongruously, there is global absence of a harmonized policy direction; capable of providing the required indicators on climate policies for monitoring sustainability of international agricultural development projects. We conduct extensive review and synthesis on existing limitations on global climate policy governance, agricultural food security and sustainability of international agricultural development projects, and conjecture the role of non-state and sub-national climate stakeholder engagements, and monitoring and evaluation strategies for improved climate policy action for sustaining international agricultural development projects.

Keywords: climate policy, agriculture, development projects, sustainability

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Authors: Abdulrahman M. Qahtani, Gary. B. Wills, Andy. M. Gravell

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Communicating and managing customers’ requirements in software development projects play a vital role in the software development process. While it is difficult to do so locally, it is even more difficult to communicate these requirements over distributed boundaries and to convey them to multiple distribution customers. This paper discusses the communication of multiple distribution customers’ requirements in the context of customised software products. The main purpose is to understand the challenges of communicating and managing customisation requirements across distributed boundaries. We propose a model for Communicating Customisation Requirements of Multi-Clients in a Distributed Domain (CCRD). Thereafter, we evaluate that model by presenting the findings of a case study conducted with a company with customisation projects for 18 distributed customers. Then, we compare the outputs of the real case process and the outputs of the CCRD model using simulation methods. Our conjecture is that the CCRD model can reduce the challenge of communication requirements over distributed organisational boundaries, and the delay in decision making and in the entire customisation process time.

Keywords: customisation software products, global software engineering, local decision making, requirement engineering, simulation model

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Authors: Konstanca Nikolajevic, Nicolas Belanger, David Duvivier, Rabie Ben Atitallah, Abdelhakim Artiba

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Finding the optimal 3D path of an aerial vehicle under flight mechanics constraints is a major challenge, especially when the algorithm has to produce real-time results in flight. Kinematics models and Pythagorian Hodograph curves have been widely used in mobile robotics to solve this problematic. The level of difficulty is mainly driven by the number of constraints to be saturated at the same time while minimizing the total length of the path. In this paper, we suggest a pragmatic algorithm capable of saturating at the same time most of dimensioning helicopter 3D trajectories’ constraints like: curvature, curvature derivative, torsion, torsion derivative, climb angle, climb angle derivative, positions. The trajectories generation algorithm is able to generate versatile complex 3D motion primitives feasible by a helicopter with parameterization of the curvature and the climb angle. An upper ”motion primitives’ concatenation” algorithm is presented based. In this article we introduce a new way of designing three-dimensional trajectories based on what we call the ”Dubins gliding symmetry conjecture”. This extremely performing algorithm will be soon integrated to a real-time decisional system dealing with inflight safety issues.

Keywords: robotics, aerial robots, motion primitives, helicopter

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Authors: JoVontae Butts

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A central and enduring theme in the study of American politics is political participation, which indicates the health of a democracy, citizen buy-in, and fair political representation. Though voting push factors have been thoroughly researched and are becoming better understood, the effect of those same push factors often varies for marginalized people. Black voters begun to cast votes at a steadily increasing rate following the 1996 election, gradually growing to its highest level in the 2012 presidential election, even surpassing white voter participation rates. The thirty-year growth period of Black voter engagement concluded in the 2016 election, with the number of participating Black voters stumbling by approximately 7% while other demographics remained roughly the same. Theories for the shift in Black voter behavior range from vote suppression to discouragement due to Barack Obama’s concluding tenure in office. Furthermore, Black voter engagement rebounded in the 2020 election, leaving turnout and race scholars to speculate even further, predicting that disapproval of Trump energized the Black voter bloc. Though there is much conjecture regarding the changes in Black voter behavior, there is truly little empirical evidence to vet those suppositions. This study engages and quantifies speculations for the changes in Black voter engagement in recent elections using 2016 and 2020 American National Election Studies Pilot Study data. Additionally, this study expands upon McGregor’s theory of political hypervigilance by exploring differences in political engagement for church-attending Black voters and those that do not.

Keywords: race, religion, evangelicalism, political engagement

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Authors: Catarina Cruz, Ana Breda

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Tiling problems have been capturing the attention of many mathematicians due to their real-life applications. In this study, we deal with tilings of Zⁿ by Lee spheres, where n is a positive integer number, being these tilings related with error correcting codes on the transmission of information over a noisy channel. We focus our attention on the question ‘for what values of n and r does the n-dimensional Lee sphere of radius r tile Zⁿ?’. It seems that the n-dimensional Lee sphere of radius r does not tile Zⁿ for n ≥ 3 and r ≥ 2. Here, we prove that is not possible to tile Z⁷ with Lee spheres of radius 2 presenting a proof based on a combinatorial method and faithful to the geometric idea of the problem. The non-existence of such tilings has been studied by several authors being considered the most difficult cases those in which the radius of the Lee spheres is equal to 2. The relation between these tilings and error correcting codes is established considering the center of a Lee sphere as a codeword and the other elements of the sphere as words which are decoded by the central codeword. When the Lee spheres of radius r centered at elements of a set M ⊂ Zⁿ tile Zⁿ, M is a perfect r-error correcting Lee code of word length n over Z, denoted by PL(n, r). Our strategy to prove the non-existence of PL(7, 2) codes are based on the assumption of the existence of such code M. Without loss of generality, we suppose that O ∈ M, where O = (0, ..., 0). In this sense and taking into account that we are dealing with Lee spheres of radius 2, O covers all words which are distant two or fewer units from it. By the definition of PL(7, 2) code, each word which is distant three units from O must be covered by a unique codeword of M. These words have to be covered by codewords which dist five units from O. We prove the non-existence of PL(7, 2) codes showing that it is not possible to cover all the referred words without superposition of Lee spheres whose centers are distant five units from O, contradicting the definition of PL(7, 2) code. We achieve this contradiction by combining the cardinality of particular subsets of codewords which are distant five units from O. There exists an extensive literature on codes in the Lee metric. Here, we present a new approach to prove the non-existence of PL(7, 2) codes.

Keywords: Golomb-Welch conjecture, Lee metric, perfect Lee codes, tilings

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Authors: Dominic McGann

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Applying Kuhn’s model of paradigm shifts in science to cases of doctrinal change in religion has been a common area of study in recent years. Few authors, however, have sought an explanation for the ease with which this model of theory change in science can be applied to cases of religious change. In order to provide such an explanation of this analytic phenomenon, this paper aims to answer one central question: Why is it that a theory that was intended to be used in an analysis of the history of science can be applied to something as disparate as the doctrinal history of religion with little to no modification? By way of answering this question, this paper begins with an explanation of Kuhn’s model and its applications in the field of religious studies. Following this, Massa’s recently proposed explanation for this phenomenon, and its notable flaws will be explained by way of framing the central proposal of this article, that the operative parts of scientific and religious changes function on the same fundamental concept of changes in understanding. Focusing its argument on this key concept, this paper seeks to illustrate its operation in cases of religious conversion and in Kuhn’s notion of the incommensurability of different scientific paradigms. The conjecture of this paper is that just as a Pagan-turned-Christian ceases to hear Thor’s hammer when they hear a clap of thunder, so too does a Ptolemaic-turned-Copernican-astronomer cease to see the Sun orbiting the Earth when they view a sunrise. In both cases, the agent in question has undergone a similar change in universal understanding, which provides us with a fundamental connection between changes in religion and changes in science. Following an exploration of this connection, this paper will consider the implications that such a connection has for the concept of the division between religion and science. This will, in turn, lead to the conclusion that religion and science are more alike than they are opposed with regards to the fundamental notion of understanding, thereby providing an answer to our central question. The major finding of this paper is that Kuhn’s model can be applied to religious cases so easily because changes in science and changes in religion operate on the same type of change in understanding. Therefore, in summary, science and religion share a crucial similarity and are not as disparate as they first appear.

Keywords: Thomas Kuhn, science and religion, paradigm shifts, incommensurability, insight and understanding, philosophy of science, philosophy of religion

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Authors: Stephens Oluyemi Adetunji, Nel Norma Margaret, Naidu Narainsamy

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Empathy has been identified by researchers to be a crucial factor in helping adolescents to refrain from delinquent behavior. Adolescent delinquent behavior is a social problem that has become a source of concern to parents, psychologists, educators, correctional services, researchers as well as governments of nations. Empathy is a social skill that enables an individual to understand and to share another’s emotional state. An individual with a high level of empathy will avoid any act or behavior that will affect another person negatively. The need for this study is predicated on the fact that delinquent adolescent behavior could lead to adult criminality. This, in the long run, has the potential of resulting in an increase in crime rate thereby threatening public safety. It has therefore become imperative to explore the level of empathy of delinquent adolescents who have committed crime and are awaiting trial. It is the conjecture of this study that knowledge of the empathy level of delinquent adolescents will provide an opportunity to design an intervention strategy to remediate the deficit. This study was therefore designed to determine the level of empathy of delinquent adolescents. In addition, this study provides a better understanding of factors that may prevent adolescents from developing delinquent behavior, in this case, delinquents’ empathy levels. In the case of participants who have a low level of empathy, remediation strategies to improve their empathy level would be designed. Two research questions were raised to guide this study. A mixed methods research design was employed for the study. The sample consists of fifteen male adolescents who are between 13-18 years old with a mean age of 16.5 years old. The participants are adolescents who are awaiting trial. The non-probability sampling technique was used to obtain the sample for the quantitative study while purposive sampling was used in the case of the qualitative study. A self–report questionnaire and structured interview were used to assess the level of empathy of participants. The data obtained was analysed using the simple percentages for the quantitative data and transcribing the qualitative data. The result indicates that most of the participants have low level of empathy. It is also revealed that there is a difference in the empathy level on the basis of whether they are from parents living together and those whose parents are separated. Based on the findings of this study, it is recommended that the level of empathy of participants be improved through training and emphasizing the importance of stimulating family environment for children. It is also recommended that programs such as youth mentoring and youth sheltering be established by the government of South Africa to address the menace of delinquent adolescents.

Keywords: adolescents, behavior, delinquents, empathy

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Authors: Krupali Mehta, Sandip Bhatt, Umesh Trivedi, Bhavesh Bharatiya, Mukesh Ranjan, Atindra D. Shukla

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Owing to the dominating surface forces and large-scale surface interactions, the nano-scale particles face difficulties in getting suspended in various media. Magnetic nanoparticles of iron oxide offer a great deal of promise due to their ease of preparation, reasonable magnetic properties, low cost and environmental compatibility. We intend to modify the surface of magnetic Fe₂O₃ nanoparticles with selected surface modifying agents using simple and effective single-step chemical reactions in order to enhance dispersibility of magnetic nanoparticles in non-polar media. Magnetic particles were prepared by hydrolysis of Fe²⁺/Fe³⁺ chlorides and their subsequent oxidation in aqueous medium. The dried particles were then treated with Octadecyl quaternary ammonium silane (Terrasil™), stearic acid and gallic acid ester of stearyl alcohol in ethanol separately to yield S-2 to S-4 respectively. The untreated Fe₂O₃ was designated as S-1. The surface modified nanoparticles were then analysed with Dynamic Light Scattering (DLS), Fourier Transform Infrared spectroscopy (FTIR), X-Ray Diffraction (XRD), Thermogravimetric Gravimetric Analysis (TGA) and Scanning Electron Microscopy and Energy dispersive X-Ray analysis (SEM-EDAX). Characterization reveals the particle size averaging 20-50 nm with and without modification. However, the crystallite size in all cases remained ~7.0 nm with the diffractogram matching to Fe₂O₃ crystal structure. FT-IR suggested the presence of surfactants on nanoparticles’ surface, also confirmed by SEM-EDAX where mapping of elements proved their presence. TGA indicated the weight losses in S-2 to S-4 at 300°C onwards suggesting the presence of organic moiety. Hydrophobic character of modified surfaces was confirmed with contact angle analysis, all modified nanoparticles showed super hydrophobic behaviour with average contact angles ~129° for S-2, ~139.5° for S-3 and ~151° for S-4. This indicated that surface modified particles are super hydrophobic and they are easily dispersible in non-polar media. These modified particles could be ideal candidates to be suspended in oil-based fluids, polymer matrices, etc. We are pursuing elaborate suspension/sedimentation studies of these particles in various oils to establish this conjecture.

Keywords: iron nanoparticles, modification, hydrophobic, dispersion

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Authors: Lerato Dixon, Thorsten Chmura

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This paper explores whether ethnic identity in Zimbabwe leads to discriminatory behaviour and the degree to which a norm-based intervention can shift this discriminatory behaviour. Social Identity Theory suggests that group identity can lead to favouritism towards the in-group and discriminatory behaviour towards the out-group. Agents yield higher utility from maintaining positive self-esteem by confirming with group behaviour. This paper focuses on the two majority ethnic groups in Zimbabwe – the Ndebele and Shona. Racial identities are synonymous with the language spoken. Zimbabwe’s history highlights how identity formation took place. As following independence, political parties became recognised as either Ndebele or Shona-speaking. It is against this backdrop that this study investigates the degree to which norm-based nudge can alter behaviour. This paper uses experimental methods to analyse discriminatory behaviour between two naturally occurring ethnic groups in Zimbabwe. In addition, we investigate if social norm-based interventions can shift discriminatory behaviour to understand if the divide between these two identity groups can be further divided or healed. Participants are randomly assigned into three groups to receive information regarding a social norm. We compare the effect of a proscriptive social norm-based intervention, stating what shouldn't be done and prescriptive social norms as interventions, stating what should be done. Specifically, participants are either shown the socially appropriate (Heal) norm, the socially inappropriateness (Divide) norm regarding interethnic marriages or no norm-based intervention. Following the random assignment into intervention groups, participants take part in the Trust Game. We conjecture that discrimination will shift in accordance with the prevailing social norm. Instead, we find evidence of interethnic discriminatory behaviour. We also find that trust increases when interacting with Ndebele, Shona and Zimbabwean participants following the Heal intervention. However, if the participant is Shona, the Heal intervention decreases trust toward in-groups and Zimbabwean co-players. On the other hand, if the participant is Shona, the Divide treatment significantly increases trust toward Ndebele participants. In summary, we find evidence that norm-based interventions significantly change behaviour. However, the prescriptive norm-based intervention (Heal) decreases trust toward the in-group, out-group and national identity group if the participant is Shona – therefore having an adverse effect. In contrast, the proscriptive Divide treatment increases trust if the participant is Shona towards Ndebele co-players. We conclude that norm-based interventions have a ‘rebound’ effect by altering behaviour in the opposite direction.

Keywords: discrimination, social identity, social norm-based intervention, zimbabwe

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Authors: Wayne Tarrant, Ethan Petersen

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The concept of a flat tax goes back to at least the Biblical tithe. A progressive income tax was first vociferously espoused in a small, but famous, pamphlet in 1848 (although England had an emergency progressive tax for war costs prior to this). Within a few years many countries had adopted the progressive structure. The flat tax was only reinstated in some small countries and British protectorates until Mart Laar was elected Prime Minister of Estonia in 1992. Since Estonia’s adoption of the flat tax in 1993, many other formerly Communist countries have likewise abandoned progressive income taxes. Economists had expectations of what would happen when a flat tax was enacted, but very little work has been done on actually measuring the effect. With a testbed of 21 countries in this region that currently have a flat tax, much comparison is possible. Several countries have retained progressive taxes, giving an opportunity for contrast. There are also the cases of Czech Republic and Slovakia, which have adopted and later abandoned the flat tax. Further, with over 20 years’ worth of economic history in some flat tax countries, we can begin to do some serious longitudinal study. In this paper we consider many economic variables to determine if there are statistically significant differences from before to after the adoption of a flat tax. We consider unemployment rates, tax receipts, GDP growth, Gini coefficients, and market data where the data are available. Comparisons are made through the use of event studies and time series methods. The results are mixed, but we draw statistically significant conclusions about some effects. We also look at the different implementations of the flat tax. In some countries there are equal income and corporate tax rates. In others the income tax has a lower rate, while in others the reverse is true. Each of these sends a clear message to individuals and corporations. The policy makers surely have a desired effect in mind. We group countries with similar policies, try to determine if the intended effect actually occurred, and then report the results. This is a work in progress, and we welcome the suggestion of variables to consider. Further, some of the data from before the fall of the Iron Curtain are suspect. Since there are new ruling regimes in these countries, the methods of computing different statistical measures has changed. Although we first look at the raw data as reported, we also attempt to account for these changes. We show which data seem to be fictional and suggest ways to infer the needed statistics from other data. These results are reported beside those on the reported data. Since there is debate about taxation structure, this paper can help inform policymakers of change the flat tax has caused in other countries. The work shows some strengths and weaknesses of a flat tax structure. Moreover, it provides beginnings of a scientific analysis of the flat tax in practice rather than having discussion based solely upon theory and conjecture.

Keywords: flat tax, financial markets, GDP, unemployment rate, Gini coefficient

Procedia PDF Downloads 339

Authors: O. B. Iskender, K. V. Ling, V. Dubanchet, L. Simonini

Abstract:

This paper discusses the recent advances and future prospects of spacecraft position and attitude control using Model Predictive Control (MPC). First, the challenges of the space missions are summarized, in particular, taking into account the errors, uncertainties, and constraints imposed by the mission, spacecraft and, onboard processing capabilities. The summary of space mission errors and uncertainties provided in categories; initial condition errors, unmodeled disturbances, sensor, and actuator errors. These previous constraints are classified into two categories: physical and geometric constraints. Last, real-time implementation capability is discussed regarding the required computation time and the impact of sensor and actuator errors based on the Hardware-In-The-Loop (HIL) experiments. The rationales behind the scenarios’ are also presented in the scope of space applications as formation flying, attitude control, rendezvous and docking, rover steering, and precision landing. The objectives of these missions are explained, and the generic constrained MPC problem formulations are summarized. Three key design elements used in MPC design: the prediction model, the constraints formulation and the objective cost function are discussed. The prediction models can be linear time invariant or time varying depending on the geometry of the orbit, whether it is circular or elliptic. The constraints can be given as linear inequalities for input or output constraints, which can be written in the same form. Moreover, the recent convexification techniques for the non-convex geometrical constraints (i.e., plume impingement, Field-of-View (FOV)) are presented in detail. Next, different objectives are provided in a mathematical framework and explained accordingly. Thirdly, because MPC implementation relies on finding in real-time the solution to constrained optimization problems, computational aspects are also examined. In particular, high-speed implementation capabilities and HIL challenges are presented towards representative space avionics. This covers an analysis of future space processors as well as the requirements of sensors and actuators on the HIL experiments outputs. The HIL tests are investigated for kinematic and dynamic tests where robotic arms and floating robots are used respectively. Eventually, the proposed algorithms and experimental setups are introduced and compared with the authors' previous work and future plans. The paper concludes with a conjecture that MPC paradigm is a promising framework at the crossroads of space applications while could be further advanced based on the challenges mentioned throughout the paper and the unaddressed gap.

Keywords: convex optimization, model predictive control, rendezvous and docking, spacecraft autonomy

Procedia PDF Downloads 110

Authors: Lei Li, Ming M. Chai, Xiao X. Lu, Jia W. Wang

Abstract:

The mixing process of two liquid layers in a cylindrical container includes the upper liquid with higher density rushing into the lower liquid with lighter density, the lower liquid rising into the upper liquid, meanwhile the two liquid layers having interactions with each other, forming vortices, spreading or dispersing in others, entraining or mixing with others. It is a complex process constituted of flow instability, turbulent mixing and other multiscale physical phenomena and having a fast evolution velocity. In order to explore the mechanism of the process and make further investigations, some experiments about the interfacial instability and mixing behavior between two liquid layers bounded in different volumes are carried out, applying the planar laser induced fluorescence (PLIF) and the high speed camera (HSC) techniques. According to the results, the evolution of interfacial instability between immiscible liquid develops faster than theoretical rate given by the Rayleigh-Taylor Instability (RTI) theory. It is reasonable to conjecture that some mechanisms except the RTI play key roles in the mixture process of two liquid layers. From the results, it is shown that the invading velocity of the upper liquid into the lower liquid does not depend on the upper liquid's volume (height). Comparing to the cases that the upper and lower containers are of identical diameter, in the case that the lower liquid volume increases to larger geometric space, the upper liquid spreads and expands into the lower liquid more quickly during the evolution of interfacial instability, indicating that the container wall has important influence on the mixing process. In the experiments of miscible liquid layers’ mixing, the diffusion time and pattern of the liquid interfacial mixing also does not depend on the upper liquid's volumes, and when the lower liquid volume increases to larger geometric space, the action of the bounded wall on the liquid falling and rising flow will decrease, and the liquid interfacial mixing effects will also attenuate. Therefore, it is also concluded that the volume weight of upper heavier liquid is not the reason of the fast interfacial instability evolution between the two liquid layers and the bounded wall action is limited to the unstable and mixing flow. The numerical simulations of the immiscible liquid layers’ interfacial instability flow using the VOF method show the typical flow pattern agree with the experiments. However the calculated instability development is much slower than the experimental measurement. The numerical simulation of the miscible liquids’ mixing, which applying Fick’s diffusion law to the components’ transport equation, shows a much faster mixing rate than the experiments on the liquids’ interface at the initial stage. It can be presumed that the interfacial tension plays an important role in the interfacial instability between the two liquid layers bounded in finite volume.

Keywords: interfacial instability and mixing, two liquid layers, Planar Laser Induced Fluorescence (PLIF), High Speed Camera (HSC), interfacial energy and tension, Cahn-Hilliard Navier-Stokes (CHNS) equations

Procedia PDF Downloads 248