Analysis of the Hexagonal Split Ring Resonator using Machine Learning by Considering Split Gap as a Prime Factor

The Hexagonal split-ring resonators (HSRR) are one of the prime elements of metamaterial and patch antenna design in the millimetre-wave range. Even though it's widely used there is no particular mathematic model is available for it. This analysis presents the mathematical nature of the relation between split widths, resonance frequencies; reflection (s11) and mutual coupling (s12) by identifying tend of the data with the aid of machine learning algorithms. The predicted relation will help to design efficient metamaterial, antennas and related appliances.

COMPLETELY PRIME ONE-SIDED IDEALS IN SKEW POLYNOMIAL RINGS

Let R = K[x, σ] be the skew polynomial ring over a field K, where σ is an automorphism of K of finite order. We show that prime elements in R correspond to completely prime one-sided ideals – a notion introduced by Reyes in 2010. This extends the natural correspondence between prime elements and prime ideals in commutative polynomial rings.

Materialism and Legal Historiography, from Bachelard to Benjamin

As the linguistic/cultural turn of the last fifty years has begun to ebb, sociolegal and legal-humanist scholarship has seen an accelerating return to materiality. This chapter asks what relationship may be forthcoming between the “new materialisms” and “vibrant matter” of recent years, and the older materialisms—both historical and literary, both Marxist and non-Marxist—that held sway prior to post-structuralism. What impact might such a relationship have on the forms, notably “spatial justice,” that materiality is assuming in contemporary legal studies? To attempt answers, the chapter turns to two figures from more than half a century ago: Gaston Bachelard—once famous, now mostly forgotten; and Walter Benjamin—once largely forgotten, now famous. A prolific and much-admired writer between 1930 and 1960, Bachelard pursued two trajectories of inquiry: a dialectical and materialist and historical (but non-Marxist) philosophy of science; and a poetics of the material imagination based on inquiry into the literary reception and representation of the prime elements—earth, water, fire, and air. Between the late 1920s and 1940, meanwhile, Benjamin developed an idiosyncratic but potent form of historical materialism dedicated to “arousing [the world] from its dream of itself.” The chapter argues that by mobilizing Bachelard and Benjamin for scholarship at the intersection of law and the humanities, old and new materialisms can be brought into a satisfying conjunction that simultaneously offers a poetics for spatial justice and lays a foundation for a materialist legal historiography for the twenty-first century.

Travel back to school: use of humour in intertwining of objective authenticity and staged experiences

From living museums to heritage escape rooms, edutainment is becoming a norm in interpretation of heritage, yet not much is known, of the specific role humour plays in the creation and performance of such educational products. This paper explores concepts of authenticity, functions of humour and experience design dimensions on an in-depth case study of a tourism product. The product “Smart Head Primary School” is a re-enactment of teaching as it occurred in the 1950’s in Slovenia. It gained a high extent of popularity primarily due to its extensive inclusion of humour. The product uses the role of a strict teacher to interpret to the “pupils” (visitors) the prime elements of the regions’ heritage. To analyse the intertwining of humour with heritage interpretation, the authors combine two research methods: (a) the in-depth analysis of a transcribed video-recording of a sample performance including the self-analysis and the reflections by one of the “teachers” and (b) a survey distributed to the visitors of the product. The results show that with the use of humour, visitors are able to perceive and recognize the difference between objective and constructive authenticity more effectively.

Does the Homogeneous City Belong to the Past?

As the case of Paris embodies, a whole culture of the European city has built its identity and organized the collective life of its inhabitants on the idea of homogeneity. The homogeneous city has thus significantly contributed to the collective self-representation through housing architecture. The strong degree of homogeneity of the nineteenth-century European city undoubtedly represents one of the most vivid examples of an architectural self-celebrating collective moment. This singular urban coherence is one of the few attributes of the traditional city spared by the Avant-gardes in the early twentieth century, for its ability to absorb a large number of variations without compromising the expression of continuity. A careful reading of their three main housing models—the Siedlung, the Hof and the Garden City—could confirm such a perspective, as do Existenzminimum standards. This long-standing tradition now seems to have been broken, since the homogeneous city is no longer considered as a current operating principle for urban planning. In order to understand—and perhaps overcome—the reasons for such resistance to one of the prime elements of European urban history, this article proposes to review its evolution over the last two centuries, focusing on the importance given to housing in the establishment, and the criticism and potential renegotiation of homogeneity as a malleable and latent principle.

Conjetura de GOLDBACH, números naturales y teorema de números primos

Mediante el uso de Geogebra en el siguiente manuscrito se realiza un análisis de la conjetura de Goldbach, posteriormente se comprueba mediante expresiones algebraicas que siempre existe una cantidad mínima de elementos primos que hacen que se cumpla la conjetura para cualquier número natural par . Se toma en consideración el gráfico que es generado mediante el Método Gráfico de la Conjetura de Goldbach, en el que se examinan cada una de las variables que intervienen en el eje de las ordenadas y las abscisas. Luego de esto, se estudian ciertos números pares conocidos en los que se sabe la cantidad de primos existentes, posteriormente se separa a cualquier número en intervalos desde 1 a y desde N hasta , encontrando así que la cantidad de primos en el primer intervalo mencionado es superior a la cantidad de elementos primos del segundo, con estos resultados y el análisis realizado a la gráfica del Método Gráfico antes mencionado, se llega a la conclusión que la distribución de los primos está relacionada con la función logaritmo natural; tal como está expresado en el Teorema de los Números Primos , pero en este caso; con una ligera variante para cada uno de los intervalos antes mencionados. Se realiza posteriormente un análisis de probabilidad que comprueba que la cantidad de intersecciones que se producen está intrínsecamente relacionada con las funciones que limitan la cantidad de elementos primos, que esto a su vez también se relaciona con la función propuesta por Gauss. Palabras clave: Conjetura Goldbach, Teorema, números primos. Abstract: By using Geogebra in the following manuscript, an analysis of the Goldbach conjecture is made. It has been verified through algebraic expressions that there is always a minimum amount of prime elements that make the conjecture for any natural pair number . The graph that is generated by the Graphical Method of the Goldbach Conjecture is taken into consideration, in which the variables that intervene in the axis of the ordinates and the abscissas are examined. After this, certain known even numbers were studied which the number of existing prime numbers is known. Later, it is separated from any number in intervals from 1 to and from N to , thus, finding the prime numbers in the first one. The aforementioned interval is greater than the number of prime elements of the second, with these results and the analysis made to the graph of the aforementioned Graphic Method, it is concluded that the distribution of the primes is related to the natural logarithm function; as it is expressed in the Theorem of the Prime Numbers, but in this case with a slight variant for each of the aforementioned intervals. A probability analysis to verify that the number of intersections that occur is intrinsically related to the function that limits the number of prime elements was performed. This is also related to the function proposed by Gauss. Key words: Goldbach conjecture, Prime number, theorem.