Toric rings, inseparability and rigidity

This article provides the basic algebraic background on infinitesimal deformations and presents the proof of the well-known fact that the non-trivial infinitesimal deformations of a $K$-algebra $R$ are parameterized by the elements of cotangent module $T^1(R)$ of $R$. In this article we focus on deformations of toric rings, and give an explicit description of $T^1(R)$ in the case that $R$ is a toric ring. In particular, we are interested in unobstructed deformations which preserve the toric structure. Such deformations we call separations. Toric rings which do not admit any separation are called inseparable. We apply the theory to the edge ring of a finite graph. The coordinate ring of a convex polyomino may be viewed as the edge ring of a special class of bipartite graphs. It is shown that the coordinate ring of any convex polyomino is inseparable. We introduce the concept of semi-rigidity, and give a combinatorial description of the graphs whose edge ring is semi-rigid. The results are applied to show that for $m-k=k=3$, $G_{k,m-k}$ is not rigid while for $m-k\geq k\geq 4$, $G_{k,m-k}$ is rigid. Here $G_{k,m-k}$ is the complete bipartite graph $K_{m-k,k}$ with one edge removed.Comment: 33 pages, chapter 2 of the Book << Multigraded Algebra and Applications>> 2018, Springer International Publishing AG, part of Springer Natur

The Theory of Factions in Monopoly Capital

Kurt Gossweiler has become known as one of the most important German researchers on fascism. Particularly his books The Röhm Affair, Big Banks, Industrial Monopolies, State: Economy and Policy of the State Monopolistic Capitalism in Germany 1914–1932 and Capital, Reichswehr and NSDAP: To the Early History of German Fascism 1919–1924 are found as reference books also in Western German university libraries, despite Gossweiler's main merit: having irrefutably hammered out the class character of fascism analyzing the factions in German monopoly capitalism. After 1989, after the incorporation of the socialist German Democratic Republic (GDR), he devoted himself to researching the causes of the collapse of the Soviet Union and its impact with focus on revisionism. </p

FINANCIAL AND CURRENCY CRISIS UNDERMINES THE EURO AND NATIONAL SOVEREIGNTY

The euro crisis reveals that, under imperialist conditions, oppressor nations developed and they are oppressing other nations. Less money capital of "rentiers" and "usurers" finds its way into the sphere of production to extract surplus value, but circulates in the financial sector as "fictitious capital" instead. The financial crisis shows where wealth is produced and how the capitalist crisis starting in the sphere of production, penetrated the financial sector and from there the most powerful EU states too. To rescue the rich, governments try to pass on the losses to the working people and the poor. The imperialist states try to pass on the burden to the weaker states, denying their national sovereignty. When the working class and the peoples organize resistance, the struggle amongst monopolies and national states over sharing the wealth and passing on the losses becomes fierce. The danger of fascism and war grows

Subprime Crisis and Marx's Theory on Ground Rent

Most studies of the subprime crisis have taken into account the significance of the banks in general but not the specifically important role of mortgage loans including the crucial factor of private landed property. Marx's theory on ground rent serves as a key in a deeper understanding of the subprime crisis and in differentiating the class interests. Referring to Marx's theory on ground rent especially the topics of landed property, differential and absolute rent, price of land, mortgage, and fictitious capital, an analysis is given of the consequences of ground rent under monopolist capitalism, in particular on the recent subprime crisis, which has its winners and losers. The article concludes with the bourgeois and the proletarian solution of private landed property

Eliciting a predatory response in the eastern corn snake (Pantherophis guttatus) using live and inanimate sensory stimuli: implications for managing invasive populations

North America's Eastern corn snake (Pantherophis guttatus) has been introduced to several islands throughout the Caribbean and Australasia where it poses a significant threat to native wildlife. Invasive snake control programs often involve trapping with live bait, a practice that, as well as being costly and labour intensive, raises welfare and ethical concerns. This study assessed corn snake response to live and inanimate sensory stimuli in an attempt to inform possible future trapping of the species and the development of alternative trap lures. We exposed nine individuals to sensory cues in the form of odour, visual, vibration and combined stimuli and measured the response (rate of tongue-flick [RTF]). RTF was significantly higher in odour and combined cues treatments, and there was no significant difference in RTF between live and inanimate cues during odour treatments. Our findings suggest chemical cues are of primary importance in initiating predation and that an inanimate odour stimulus, absent of simultaneous visual and vibratory cues, is a potential low-cost alternative trap lure for the control of invasive corn snake populations

Persistent body image disturbance following recovery from eating disorders

Background: It has been previously found that individuals with an eating disorder experience the rubber hand illusion (RHI) significantly more strongly than healthy controls on both perceptual (proprioceptive drift) and subjective (self-report embodiment questionnaire) measures. Such heightened sensitivity to visual information about the body, and reduced somatosensory information processing about the body, indicate an increased malleability of the bodily self. The aim of the present study was to explore whether this is a state or persisting/trait phenomenon. Method: The RHI and self-report measures of eating disorder psychopathology (EDI-3 subscales of Drive for Thinness, Bulimia, Body Dissatisfaction, Interoceptive Deficits, and Emotional Dysregulation; DASS-21; and the Self-Objectification Questionnaire) were administered to 78 individuals with an eating disorder, 28 individuals recovered from an eating disorder, and 61 healthy controls. Results: Proprioceptive drift in recovered individuals was intermediate between the acutely ill and HC groups. Subjective report of the strength of the illusion in recovered individuals was similar to acutely ill individuals. Discussion: These results indicate that increased malleability of the bodily self persists following recovery and may be a trait phenomenon in people with eating disorders, such that those with a lifetime history of an eating disorder may have heightened sensitivity to visual information about the body and reduced somatosensory information processing of the body

Injection of gases into the stratosphere by explosive volcanic eruptions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95018/1/jgrd10245.pd