Weighted Shift Matrices: Unitary Equivalence, Reducibility and Numerical Ranges

An $n$-by-$n$ ($n\ge 3$) weighted shift matrix $A$ is one of the form [{array}{cccc}0 & a_1 & & & 0 & \ddots & & & \ddots & a_{n-1} a_n & & & 0{array}], where the $a_j$'s, called the weights of $A$, are complex numbers. Assume that all $a_j$'s are nonzero and $B$ is an $n$-by-$n$ weighted shift matrix with weights $b_1,..., b_n$. We show that $B$ is unitarily equivalent to $A$ if and only if $b_1... b_n=a_1...a_n$ and, for some fixed $k$, $1\le k \le n$, $|b_j| = |a_{k+j}|$ ($a_{n+j}\equiv a_j$) for all $j$. Next, we show that $A$ is reducible if and only if $A$ has periodic weights, that is, for some fixed $k$, $1\le k \le \lfloor n/2\rfloor$, $n$ is divisible by $k$, and $|a_j|=|a_{k+j}|$ for all $1\le j\le n-k$. Finally, we prove that $A$ and $B$ have the same numerical range if and only if $a_1...a_n=b_1...b_n$ and $S_r(|a_1|^2,..., |a_n|^2)=S_r(|b_1|^2,..., |b_n|^2)$ for all $1\le r\le \lfloor n/2\rfloor$, where $S_r$'s are the circularly symmetric functions.Comment: 27 page

Price competition with OEM-remanufactured products

Abstract Despite environmental and economic advantages of remanufacturing, the potential for cannibalizing the sales of new product by OEM-remanufactured products is a key obstacle for OEMs to remanufacture their end-of-life products. In this paper, we investigate the OEM-remanufacturing strategy and its impacts on price decisions by adopting a game-theoretic framework, where there is competition between a remanufacturer who sells third-party remanufactured products and an OEM who offers new products and chooses whether to introduce OEM-remanufactured products. We formulate consumer valuation for the products in the consideration of consumers' perceived similarity between the new and OEM-remanufactured products and, moreover, characterize the chain members' equilibrium pricing behavior concerning the availability of used products for remanufacturing. We elaborate the impacts of the entry of the OEM-remanufactured products on equilibrium results and show that the provision of OEM-remanufactured products is not necessarily harmful to the remanufacturer especially when consumers perceive the less similarity between the OEM's products. Results of this study intend to provide managerial insights for managers response to the changes in competitive dynamics, consumer characteristics, and cost factors

Enhanced inhibitory synaptic transmission in the spinal dorsal horn mediates antinociceptive effects of TC-2559

<p>Abstract</p> <p>Background</p> <p>TC-2559 is a selective α4β2 subtype of nicotinic acetylcholine receptor (nAChR) partial agonist and α4β2 nAChR activation has been related to antinociception. The aim of this study is to investigate the analgesic effect of TC-2559 and its underlying spinal mechanisms.</p> <p>Results</p> <p>1) <it>In vivo </it>bioavailability study: TC-2559 (3 mg/kg) had high absorption rate in rats with maximal total brain concentration reached over 4.6 μM within first 15 min after administration and eliminated rapidly with brain half life of about 20 min after injection. 2) <it>In vivo </it>behavioral experiments: TC-2559 exerts dose dependent antinociceptive effects in both formalin test in mice and chronic constriction injury (CCI) model in rats by activation of α4β2 nAChRs; 3) Whole-cell patch-clamp studies in the superficial dorsal horn neurons of the spinal cord slices: perfusion of TC-2559 (2 μM) significantly increased the frequency, but not amplitude of spontaneous inhibitory postsynaptic currents (sIPSCs). The enhancement of sIPSCs was blocked by pre-application of DHβE (2 μM), a selective α4β2 nicotinic receptor antagonist. Neither the frequency nor the amplitude of spontaneous excitatory postsynaptic currents (sEPSCs) of spinal dorsal horn neurons were affected by TC-2559.</p> <p>Conclusions</p> <p>Enhancement of inhibitory synaptic transmission in the spinal dorsal horn via activation of α4β2 nAChRs may be one of the mechanisms of the antinociceptive effects of TC-2559 on pathological pain models. It provides further evidence to support the notion that selective α4β2 subtype nAChR agonist may be developed as new analgesic drug for the treatment of neuropathic pain.</p

Photometric and Spectroscopic Studies of V582 Lyr and V1016 Oph

We present new CCD photometric light curves about two eclipsing binaries of V582 Lyr and V1016 Oph. Our observations were carried out by the SARA 91.4 cm telescope of America in 2016 and the 60 cm telescope of Chile in 2018. V582 Lyr’s spectra type was classified as K5, and its radial velocity was determined using the LAMOST spectral survey. There are absorptions in the observed Hα line and excess emissions in the subtracted Hα line, which show weak chromospheric activity. We obtained the updated ephemeris information for V582 Lr and V1016 Oph, and found that their orbital periods are both decreasing.We concluded that the decreased rate is −0.474 (±0.011)Å~10−7 days yr−1 for V582 Lyr and 3.460 (±0.014)Å~10−7 days yr−1 for V1016 Oph. For V582 Lyr, the period variation was interpreted as a mass transfer from the secondary component to the primary one, and the corresponding rate is dM2/dt=−1.10 (±0.03)Å~10−7 Me yr−1. For V1016 Oph, we explain it by transferring from the primary component to the secondary one, and the corresponding rate is dM1/dt=−2.69 (±0.04)Å~10−7 Me yr−1. The photometric solution of V1016 Oph was obtained by analyzing the CCD photometry with the Wilson–Devinney program. We also obtained the orbital parameters of V1016 Oph by simultaneously analyzing our BVRI light curves and radial-velocity curve from the LAMOST low-resolution spectral survey. Finally, our orbital solution shows that they are contact eclipsing binaries with contact factors of 3.35 (±0.08)% for V582 Lyr and 41.0 (±0.1)% for V1016 Oph

Microscopic Description of Band Structure at Very Extended Shapes in the A ~ 110 Mass Region

Recent experiments have confirmed the existence of rotational bands in the A \~ 110 mass region with very extended shapes lying between super- and hyper-deformation. Using the projected shell model, we make a first attempt to describe quantitatively such a band structure in 108Cd. Excellent agreement is achieved in the dynamic moment of inertia J(2) calculation. This allows us to suggest the spin values for the energy levels, which are experimentally unknown. It is found that at this large deformation, the sharply down-sloping orbitals in the proton i_{13/2} subshell are responsible for the irregularity in the experimental J(2), and the wave functions of the observed states have a dominant component of two-quasiparticles from these orbitals. Measurement of transition quadrupole moments and g-factors will test these findings, and thus can provide a deeper understanding of the band structure at very extended shapes.Comment: 4 pages, 3 eps figures, final version accepted by Phys. Rev. C as a Rapid Communicatio

A regulatory mutant on TRIM26 conferring the risk of nasopharyngeal carcinoma by inducing low immune response.

The major histocompatibility complex (MHC) is most closely associated with nasopharyngeal carcinoma (NPC), but the complexity of its genome structure has proven challenging for the discovery of causal MHC loci or genes. We conducted a targeted MHC sequencing in 40 Cantonese NPC patients followed by a two-stage replication in 1065 NPC cases and 2137 controls of Southern Chinese descendent. Quantitative RT-PCR analysis (qRT-PCR) was used to detect gene expression status in 108 NPC and 43 noncancerous nasopharyngeal (NP) samples. Luciferase reporter assay and chromatin immunoprecipitation (ChIP) were used to assess the transcription factor binding site. We discovered that a novel SNP rs117565607_A at TRIM26 displayed the strongest association (OR = 1.909, Pcombined = 2.750 × 10-19 ). We also observed that TRIM26 was significantly downregulated in NPC tissue samples with genotype AA/AT than TT. Immunohistochemistry (IHC) test also found the TRIM26 protein expression in NPC tissue samples with the genotype AA/AT was lower than TT. According to computational prediction, rs117565607 locus was a binding site for the transcription factor Yin Yang 1 (YY1). We observed that the luciferase activity of YY1 which is binding to the A allele of rs117565607 was suppressed. ChIP data showed that YY1 was binding with T not A allele. Significance analysis of microarray suggested that TRIM26 downregulation was related to low immune response in NPC. We have identified a novel gene TRIM26 and a novel SNP rs117565607_A associated with NPC risk by regulating transcriptional process and established a new functional link between TRIM26 downregulation and low immune response in NPC