A New Conformable Fractional Derivative and Applications

This paper is motivated by some papers treating the fractional derivatives. We introduce a new definition of fractional derivative which obeys classical properties including linearity, product rule, quotient rule, power rule, chain rule, Rolle’s theorem, and the mean value theorem. The definition D α f t = lim h ⟶ 0 f t + h e α − 1 t − f t / h , for all t > 0 , and α ∈ 0,1 . If α = 0 , this definition coincides to the classical definition of the first order of the function f .

The Rule of Law in the Athenian Demokratia: Origins, History, and Oratory

<p>According to Aristotle, demokratia is an invalid form of constitution unless it operates in conjunction with the rule of law. Historically, the idea of the rule of law was connected with wealthy elites in Athens. However, after a series of upheavals between the Athenian mass and elites, the demos accepted the rule of law as a valid check on demotic power. Rule of law required legal codification, which outlined a framework within which democratic law functioned. The Athenian law court became the arena for enforcing the law, thereby ridding the city of negative socio/political influences. Hybris, political corruption, and general questions of legality all came under the power of the democratic courts of law, which exerted the legitimate power of the combined community. Nevertheless, tradition maintained a strong influence on law, especially in the law courts. Bound up in legal arguments were ideas of Athenian identity and it became accepted that the juries would assess the character of the accused against the character of the Athenian demos in the course of making its decision. Athenian elites who previously continued feuds extra-legally submitted to the law courts, which offered an arena for dispute resolution. Ultimately, the rule of law in the Athenian demokratia upheld Athenian law, created a legal framework, and allowed personal and political disputes to be settled before they dissolved into stasis, offering the Athenian demokratia its most successful mechanism for creating social, political, and legal, stability.</p>

The Rule of Law in the Athenian Demokratia: Origins, History, and Oratory

<p>According to Aristotle, demokratia is an invalid form of constitution unless it operates in conjunction with the rule of law. Historically, the idea of the rule of law was connected with wealthy elites in Athens. However, after a series of upheavals between the Athenian mass and elites, the demos accepted the rule of law as a valid check on demotic power. Rule of law required legal codification, which outlined a framework within which democratic law functioned. The Athenian law court became the arena for enforcing the law, thereby ridding the city of negative socio/political influences. Hybris, political corruption, and general questions of legality all came under the power of the democratic courts of law, which exerted the legitimate power of the combined community. Nevertheless, tradition maintained a strong influence on law, especially in the law courts. Bound up in legal arguments were ideas of Athenian identity and it became accepted that the juries would assess the character of the accused against the character of the Athenian demos in the course of making its decision. Athenian elites who previously continued feuds extra-legally submitted to the law courts, which offered an arena for dispute resolution. Ultimately, the rule of law in the Athenian demokratia upheld Athenian law, created a legal framework, and allowed personal and political disputes to be settled before they dissolved into stasis, offering the Athenian demokratia its most successful mechanism for creating social, political, and legal, stability.</p>

Predicting Spread Probability of Learning-Effect Computer Virus

With the rapid development of network technology, computer viruses have developed at a fast pace. The threat of computer viruses persists because of the constant demand for computers and networks. When a computer virus infects a facility, the virus seeks to invade other facilities in the network by exploiting the convenience of the network protocol and the high connectivity of the network. Hence, there is an increasing need for accurate calculation of the probability of computer-virus-infected areas for developing corresponding strategies, for example, based on the possible virus-infected areas, to interrupt the relevant connections between the uninfected and infected computers in time. The spread of the computer virus forms a scale-free network whose node degree follows the power rule. A novel algorithm based on the binary-addition tree algorithm (BAT) is proposed to effectively predict the spread of computer viruses. The proposed BAT utilizes the probability derived from PageRank from the scale-free network together with the consideration of state vectors with both the temporal and learning effects. The performance of the proposed algorithm was verified via numerous experiments.

Democracy

This chapter examines Reinhold Niebuhr’s anti-utopian defence of democracy, conceived primarily as a political arrangement marked by balance of power, rule by the governed, and a liberal constitutional order. Niebuhr’s democracy, however, is both a procedural form of government and a substantial ethical commitment. His essayistic style traversed disciplines in search of a pragmatic public philosophy that might navigate between hope and despair given inevitable conflict in democratic life. Pregnant with broader claims of morality and theology, his dialectical method crystallizes deep patterns of thought in what came to be known as his Christian Realism. The chapter places these views in historical context and notes their critical reception, highlighting debts to Augustinian, Marxist, Calvinist, and Kantian traditions. But the focus is normative and contemporary. Renewed questions about the uncertain prospects of democracy and its challenges suggest an opportunity to assess what is living and what is dead in Niebuhr’s influential account.

Accounting for the surface temperature persistence by using signal energy

The autocorrelation function (ACF) and its finite Fourier transform, referred to as signal energy, have been investigated using the ECMWF daily surface temperature data. ACF itself provides a measure of the influence of leading fluctuation between two different time points. Considering the decay of ACF, it is found that the scaling power-rule of ACF is only valid in a very short period, as the decay of ACF exists before it reaches a random noise state. Therefore, the method of the critical exponent of ACF is limited in the short length of the temporal interval. On the other hand, the distributions of the signal energy always show nice patterns, indicating the degree of persistence change. It is found, for a short period, that the distributions of the signal energy and the critical exponent are very similar, with a correlation coefficient over 0.97. For a longer period, though the critical exponent of ACF becomes invalid, the signal energy can always provide an effective method to investigate climate persistence in different lengths of time. In a 5-day period of boreal winter, the southern part of North America has a larger value of signal energy compared to the northern part; thus, the surface temperature is more stable in the north part. The result becomes opposite in the boreal summer. The method of signal energy can also be applied to a particular interval of time. In different temporal intervals, the signal energy presents very different results, especially over the El Nino regions

Liberalism and Modern Law of Information Age

The article is dedicated to the relevant issues of modern legal regulation of the social relations in the light of correlation of main ideas of liberalism and modern sociocultural realia. Liberalism as a concept is not unambiguous in its content, and therefore the use of this concept in each case depends on the context. It is proved that within several centuries the mankind has been establishing its legal life in the framework of liberal and legal doctrine. Liberalism determines freedom, equality, democracy and human rights as the major law-making values. It is traced how the ideas of classical liberalism (system of basic, interconnected principles of personal freedoms, inalienability of the natural rights, limited control, private ownership, distribution of power, rule of law, etc.) are reconsidered under the impact of the objective social factors and through the transformation are adjusted to the new conditions and are overhauled in the modern discourse. Modern period is characterized by the inconsistency between the fundamental provisions of liberalism, its values, and social life realia. Such inconsistency is determined by the specificity of information society, which is evident in the fact that the legal and juristic institutes of guaranteeing, insurance and protection of the mentioned values are not adjusted enough to the new realia. It is shown that the central dichotomy for modern European legal philosophy is the relationship between freedom as a liberal value and the phenomenon of total control over man, and because human rights are necessary to protect individual freedom in classical liberalism, while modern liberalism stands for guarantees and freedoms of individuals. The author underlines that in contrast to the doctrines of communism and fascism, liberalism preserves its vital force due to this flexibility, ability to adjust to the new social conditions which is testified to by various modifications of liberalism (classical, non-classical, neoliberalism). The article also addresses the issue of the «new human rights» in the information age and its correlation with the major liberal values of freedom and equality. The author also emphasizes the updating of the classical legal institutes in the 20th-21st centuries, i.e., the e-democracy phenomenon.

On structure of discrete Muchenhoupt and discrete Gehring classes

In this paper, we study the structure of the discrete Muckenhoupt class $\mathcal{A}^{p}(\mathcal{C})$ A p ( C ) and the discrete Gehring class $\mathcal{G}^{q}(\mathcal{K})$ G q ( K ) . In particular, we prove that the self-improving property of the Muckenhoupt class holds, i.e., we prove that if $u\in \mathcal{A}^{p}(\mathcal{C})$ u ∈ A p ( C ) then there exists $q< p$ q < p such that $u\in \mathcal{A}^{q}(\mathcal{C}_{1})$ u ∈ A q ( C 1 ) . Next, we prove that the power rule also holds, i.e., we prove that if $u\in \mathcal{A}^{p}$ u ∈ A p then $u^{q}\in \mathcal{A}^{p}$ u q ∈ A p for some $q>1$ q > 1 . The relation between the Muckenhoupt class $\mathcal{A}^{1}(\mathcal{C})$ A 1 ( C ) and the Gehring class is also discussed. For illustrations, we give exact values of the norms of Muckenhoupt and Gehring classes for power-low sequences. The results are proved by some algebraic inequalities and some new inequalities designed and proved for this purpose.

KEEPING COOL IN FLORIDA ASSISTED LIVING COMMUNITIES: BARRIERS TO POWER RULE IMPLEMENTATION

In 2018, in response to deaths of nursing home residents after Hurricane Irma, Governor Scott and the Florida legislature enacted an emergency power rule for nursing homes and assisted living communities (ALCs). It mandates these settings to have a generator to regulate ambient air temperatures during loss of primary power by Jan. 1, 2019. However, due to cost and supply challenges the implementation of these plans has been difficult, particularly for small and independently owned ALCs. The purpose of this mixed methods study is to determine the characteristics of ALCs that were able to comply with the rule and concerns raised by ALC administrators. Using data from state regulatory agencies on all Florida ALCs (N=3082), we determine associations between ALC characteristics (size, specialty license, low-income residents) and non-compliance to the rule, using chi-square and t-tests. Additionally, we conducted interviews and focus groups with ALC administrators (N=60) about issues of implementing their emergency power plan. A content analysis approach was used and Atlas.ti v7 was used for initial and axial coding. Some prevalent themes were issues with time frames, coordination between local and state regulations, and financial burden. Themes varied by size and organizational structure of ALCs. Results will inform policy-makers on the barriers faced by ALCs to implement a new regulation that may cause financial difficulties and compromise quality care. This study has implications related to disaster preparedness regulations and their effects on independent ALCs with fewer financial resources.