To Prove Four Color Theorem

In this paper, we give a proof for four color theorem(four color conjecture). Our proof does not involve computer assistance and the most important is that it can be generalized to prove Hadwiger Conjecture. Moreover, we give algorithms to color and test planarity of planar graphs, which can be generalized to graphs containing $K_x(x>5)$ minor. There are four parts of this paper: Part-1: To Prove Four Color Theorem Part-2: An Equivalent Statement of Hadwiger Conjecture when $k=5$ Part-3: A New Proof of Wagner's Equivalence Theorem Part-4: A Geometric View of Outerplanar GraphComment: The paper is further reduced, and each part is more self-contained, is the fina

Light axigluon and single top production at the LHC

The light axigluon model can explain the Tevatron $t\overline{t}$ forward-backward asymmetry and at the same time satisfy the constraints from the electroweak precision measurement and the $ATLAS$ and $CMS$ data, which induces the flavor changing ($FC$) couplings of axigluon with the $SM$ and new quarks. We investigate the effects of these $FC$ couplings on the s- and t-channel single top productions at the $LHC$ and the $FC$ decays $Z\rightarrow \overline{b}s+b\overline{s}$, $t\rightarrow c\gamma$ and $cg$. Our numerical results show that the light axigluon can give significantly contributions to single top production and the rare top decays $t\rightarrow c\gamma$ and $cg$.Comment: 22 pages, 8 figures; references added, contributions of new quarks to rare decay processes adde

A Cooperation-Driven ICN-based Caching Scheme for Mobile Content chunk Delivery at RAN

In order to resolve the tension between continuously growing mobile users’ demands on content access and the scarcity of the bandwidth capacity over backhaul links, we propose in this paper a fully distributed ICN-based caching scheme for content objects in Radio Access Network (RAN) at eNodeBs. Such caching scheme operates in a cooperative way within neighbourhoods, aiming to reduce cache redundancy so as to improve the diversity of content distribution. The caching decision logic at individual eNodeBs allows for adaptive caching, by taking into account dynamic context information, such as content popularity and availability. The efficiency of the proposed distributed caching scheme is evaluated via extensive simulations, which show great performance gains, in terms of a substantial reduction of backhaul content traffic as well as great improvement on the diversity of content distribution, etc

The identification of unilateral economic coercion under the principle of non-intervention

The principle of non-intervention is widely acknowledged as a fundamental rule of customary international law. Yet the principle’s contours remain ill-defined. Particularly, it is unclear when unilateral economic measures may constitute ‘coercion’ and thus violate the principle. This thesis seeks to address this problem. Through a detailed examination of the conception of the notion of economic coercion in practice, it demonstrates that, while unilateral economic coercion is universally recognised as prohibited under the non-intervention principle, the precise scope of this concept is unclear under lex lata. While non-WEOG states have advocated an expansive definition of economic coercion encompassing almost all types of economic measures, WEOG states have been reluctant to characterise economic measures as coercive, favouring a flexible definition of economic coercion to maintain their freedom to influence the policy choices of other states. Given the uncertainty reflected in practice, the thesis proceeds to establish an analytical framework to provide further guidance on the identification of economic coercion. It identifies five groups of different approaches proposed by international lawyers for determining non-forcible coercion and highlights the weaknesses of each approach. It also resorts to domestic legal regulation of coercive economic pressure to shed light on the concept of economic coercion in international law. By doing so, it observes similarities in the historical development of both regimes and identifies certain common regulatory trends. Drawing on both domestic and international legal doctrines, the thesis proposes a three-step method to identify economic coercion under the non-intervention principle. Essentially, an economic measure constitutes coercion either because (1) it falls within a specific type of measures universally recognised as coercive or (2) it breaches international obligations of the sender state towards the target state and (3) has such significant effects that the latter has no reasonable alternatives to resist

Multilevel DC-AC Converter Interface with Solar Panels

This paper presents a single-phase 11-level (5 H-bridge) cascaded multilevel DC-AC converter that has implemented a Phase Locked Loop (PLL) and Maximum Power Point Tracking (MPPT) with 5 separate solar panel DC sources. This topology upgrades the conventional 3-level Pulse Width Modulation (PWM) controlled converter with advantages such as smoother output waveforms, more flexibility in voltage range, smaller filter size, and switching angle control. Simulation results of voltage synchronization using PLL and experimental setup and results implementing the entire converter interface are also presented

Noble motives, unjustified reasoning: a comment on allegations of genocide under the convention on the prevention and punishment of the crime of genocide (Ukraine v. Russian Federation)

The International Court of Justice recently delivered its Provisional Measures Order on the Ukrainian Genocide case, demanding an immediate suspension of the Russian military operation against Ukraine. This article examines three legal issues deriving from this order. Firstly, it evaluates the establishment of the ICJ’s prima facie jurisdiction under the compromissory clause of the Convention on the Prevention and Punishment of the Crime of Genocide. It finds that the Order inexplicably departed from the ICJ’s jurisprudence in the Legality of Use of Force cases, and that the existence of indispensable external jus ad bellum issues in the present case should have deprived the ICJ of its jurisdiction. Secondly, it assesses the plausibility of the rights sought, and finds that there is no plausible right under the Convention on the Prevention and Punishment of the Crime of Genocide to be free from military attacks based on a claim of preventing and punishing, since the parties could not have intended so. Thirdly, it analyzes the link between the claimed rights and the provisional measure granted and finds that this requirement is not satisfied in this case because the provisional measure indicated will also protect a right under jus ad bellum, which falls outside the ICJ’s jurisdiction. In view of the above, this article argues that although the Order might achieve the political objective of mitigating the conflict, the ICJ’s reasoning has been unconvincing or at least incomplete in legal terms, which risks undermining the ICJ’s reputation and reliability as well as the coherence and credibility of international law

Shaping of molecular weight distribution using b-spline based predictive probability density function control

Issues of modelling and control of molecular weight distributions (MWDs) of polymerization products have been studied under the recently developed framework of stochastic distribution control, where the purpose is to design the required control inputs that can effectively shape the output probability density functions (PDFs) of the dynamic stochastic systems. The B-spline Neural Network has been implemented to approximate the function of MWDs provided by the mechanism model, based on which a new predictive PDF control strategy has been developed. A simulation study of MWD control of a pilot-plant styrene polymerization process has been given to demonstrate the effectiveness of the algorithms