Representation of SO(3) Group by a Maximally Entangled State

A representation of the SO(3) group is mapped into a maximally entangled two qubit state according to literatures. To show the evolution of the entangled state, a model is set up on an maximally entangled electron pair, two electrons of which pass independently through a rotating magnetic field. It is found that the evolution path of the entangled state in the SO(3) sphere breaks an odd or even number of times, corresponding to the double connectedness of the SO(3) group. An odd number of breaks leads to an additional $\pi$ phase to the entangled state, but an even number of breaks does not. A scheme to trace the evolution of the entangled state is proposed by means of entangled photon pairs and Kerr medium, allowing observation of the additional $\pi$ phase.Comment: 4 pages, 3 figure

An Examination of the Testing and Spacing Effects in a Middle Grades Social Studies Classroom

This study investigates the relation between review spacing and question format on student retention. Participants in an 8th grade Georgia Studies class reviewed previously learned material either in one sitting (massed review) or in multiple sessions (spaced review). Following the review, each participant answered questions either in multiple choice or short answer format. Subsequent to answering the questions, all students received feedback. One week following the completion of the reviews, students were given a post test. One month after the post test, students were given a final test. Pre-, post- and final tests were identical and no treatment occurred between the posttest and the final test. Correlational analyses of review spacing and question format suggest that spaced review is positively related to success on the posttest. There was no such finding related to massed review or question format on the posttest. Additionally, neither review spacing or question format had any correlational effect on the final test. Results suggest that spaced review is beneficial, but that the benefit is lost over time

Degree sums and subpancyclicity in line graphs

A graph is called subpancyclic if it contains a cycle of length k for each k between 3 and the circumference of the graph. In this paper, we show that if the degree sum of the vertices along each 2-path of a graph G exceeds (n+6)/2, or if the degree sum of the vertices along each 3-path of G exceeds (2n+16)/3, then its line graph L(G) is subpancyclic. Simple examples show that these bounds are best possible. Our results shed some light on the content of a famous Metaconjecture of Bondy

Rapid "Turn-on" of type 1 AGN in a quiescent early type galaxy SDSS1115+0544

We present a detailed study of a transient in the center of SDSS1115+0544 based on the extensive UV, optical, mid-IR light curves (LC) and spectra over 1200 days. The host galaxy is a quiescent early type galaxy at $z$ = 0.0899 with a blackhole mass of $2\times10^7M_\odot$. The transient underwent a 2.5 magnitude brightening over $\sim120$ days, reaching a peak $V$-band luminosity (extinction corrected) of $-20.9$ magnitude, then fading 0.5 magnitude over 200 days, settling into a plateau of $>600$ days. Following the optical brightening are the significant mid-IR flares at $3.4$ and $4.5\mu$m, with a peak time delay of $\sim180$ days. The mid-IR LCs are explained as the echo of UV photons by a dust medium with a radius of $5\times10^{17}$ cm, consistent with $\rm E(B-V)$ of 0.58 inferred from the spectra. This event is very energetic with an extinction corrected $L_{bol} \sim 4\times10^{44}$ erg s$^{-1}$. Optical spectra over 400 days in the plateau phase revealed newly formed broad H$\alpha, \beta$ emission with a FWHM of $\sim3750$ km s$^{-1}$ and narrow coronal lines such as [Fe VII], [Ne V]. This flare also has a steeply rising UV continuum, detected by multi-epoch $Swift$ data at $+700$ to $+900$ days post optical peak. The broad Balmer lines and the UV continuum do not show significant temporal variations. The slow evolving LCs over 1200 days, the constant Balmer lines and UV continuum at late-times rule out TDE and SN IIn as the physical model for this event. We propose that this event is a `turn-on' AGN, transitioning from a quiescent state to a type 1 AGN with a sub-Eddington accretion rate of $0.017M_\odot$/yr. This change occurred on a very short time scale of $\sim 120- 200$ days. The discovery of such a rapid `turn-on' AGN poses challenges to accretion disk theories and may indicate such event is not extremely rare.Comment: Comments are welcome. Emails to the first author. Accepted for publication in Ap

Darboux transformation for two component derivative nonlinear Schr\"odinger equation

In this paper, we consider the two component derivative nonlinear Schr\"{o}dinger equation and present a simple Darboux transformation for it. By iterating this Darboux transformation, we construct a compact representation for the $N-$soliton solutions.Comment: 12 pages, 2 figure

Data-Driven Integral Reinforcement Learning for Continuous-Time Non-Zero-Sum Games

This paper develops an integral value iteration (VI) method to efficiently find online the Nash equilibrium solution of two-player non-zero-sum (NZS) differential games for linear systems with partially unknown dynamics. To guarantee the closed-loop stability about the Nash equilibrium, the explicit upper bound for the discounted factor is given. To show the efficacy of the presented online model-free solution, the integral VI method is compared with the model-based off-line policy iteration method. Moreover, the theoretical analysis of the integral VI algorithm in terms of three aspects, i.e., positive definiteness properties of the updated cost functions, the stability of the closed-loop systems, and the conditions that guarantee the monotone convergence, is provided in detail. Finally, the simulation results demonstrate the efficacy of the presented algorithms

Primary hepatic neuroendocrine carcinoma: report of two cases and literature review.

Background: Primary hepatic neuroendocrine carcinoma (PHNEC) is extremely rare. The diagnosis of PHNEC remains challenging-partly due to its rarity, and partly due to its lack of unique clinical features. Available treatment options for PHNEC include surgical resection of the liver tumor(s), radiotherapy, liver transplant, transcatheter arterial chemoembolization (TACE), and administration of somatostatin analogues. Case presentation: We report two male PHNEC cases and discuss the diagnosis and treatment options. Both cases presented with abdominal pain; case two also presented with symptoms of jaundice. The initial diagnosis for both cases was poorly differentiated grade 3 small-cell neuroendocrine carcinoma, based on imaging characteristics and the pathology of liver biopsies. Final diagnoses of PHNEC were arrived at by ruling out non-hepatic origins. Case one presented with a large tumor in the right liver lobe, and the patient was treated with TACE. Case two presented with tumors in both liver lobes, invasions into the left branch of hepatic portal vein, and metastasis in the hepatic hilar lymph node. This patient was ineligible for TACE and was allergic to the somatostatin analogue octreotide. This limited treatment options to supportive therapies such as albumin supplementation for liver protection. Patient one and two died at 61 and 109 days, respectively, following initial hospital admission. Conclusions: We diagnosed both cases with poorly differentiated grade 3 small-cell PHNEC through imaging characteristics, immunohistochemical staining of liver biopsies, and examinations to eliminate non-hepatic origins. Neither TACE nor liver protection appeared to significantly extend survival time of the two patients, suggesting these treatments may be inadequate to improve survival of patients with poorly differentiated grade 3 small-cell PHNEC. The prognosis of poorly differentiated grade 3 small-cell PHNEC is poor due to limited and ineffective treatment options. BMC Clin Pathol 2018 Mar 1; 18:3