About multiplicities and applications to Bezout numbers

Let $(A,\mathfrak{m},\Bbbk)$ denote a local Noetherian ring and $\mathfrak{q}$ an ideal such that $\ell_A(M/\mathfrak{q}M) < \infty$ for a finitely generated $A$-module $M$. Let \au = a_1,\ldots,a_d denote a system of parameters of $M$ such that $a_i \in \mathfrak{q}^{c_i} \setminus \mathfrak{q}^{c_i+1}$ for $i=1,\ldots,d$. It follows that \chi := e_0(\au;M) - c \cdot e_0(\mathfrak{q};M) \geq 0, where $c = c_1\cdot \ldots \cdot c_d$. The main results of the report are a discussion when $\chi = 0$ resp. to describe the value of $\chi$ in some particular cases. Applications concern results on the multiplicity e_0(\au;M) and applications to Bezout numbers.Comment: 11 pages, to appear Springer INdAM-Series, Vol. 20 (2017

Towards a SDLCQ test of the Maldacena Conjecture

We consider the Maldacena conjecture applied to the near horizon geometry of a D1-brane in the supergravity approximation and present numerical results of a test of the conjecture against the boundary field theory calculation using DLCQ. We previously calculated the two-point function of the stress-energy tensor on the supergravity side; the methods of Gubser, Klebanov, Polyakov, and Witten were used. On the field theory side, we derived an explicit expression for the two-point function in terms of data that may be extracted from the supersymmetric discrete light cone quantization (SDLCQ) calculation at a given harmonic resolution. This yielded a well defined numerical algorithm for computing the two-point function. For the supersymmetric Yang-Mills theory with 16 supercharges that arises in the Maldacena conjecture, the algorithm is perfectly well defined; however, the size of the numerical computation prevented us from obtaining a numerical check of the conjecture. We now present numerical results with approximately 1000 times as many states as we previously considered. These results support the Maldacena conjecture and are within $10-15$ of the predicted numerical results in some regions. Our results are still not sufficient to demonstrate convergence, and, therefore, cannot be considered to a numerical proof of the conjecture. We present a method for using a ``flavor'' symmetry to greatly reduce the size of the basis and discuss a numerical method that we use which is particularly well suited for this type of matrix element calculation.Comment: 10 pages, 1 figur

Spectral stability of noncharacteristic isentropic Navier-Stokes boundary layers

Building on work of Barker, Humpherys, Lafitte, Rudd, and Zumbrun in the shock wave case, we study stability of compressive, or "shock-like", boundary layers of the isentropic compressible Navier-Stokes equations with gamma-law pressure by a combination of asymptotic ODE estimates and numerical Evans function computations. Our results indicate stability for gamma in the interval [1, 3] for all compressive boundary-layers, independent of amplitude, save for inflow layers in the characteristic limit (not treated). Expansive inflow boundary-layers have been shown to be stable for all amplitudes by Matsumura and Nishihara using energy estimates. Besides the parameter of amplitude appearing in the shock case, the boundary-layer case features an additional parameter measuring displacement of the background profile, which greatly complicates the resulting case structure. Moreover, inflow boundary layers turn out to have quite delicate stability in both large-displacement and large-amplitude limits, necessitating the additional use of a mod-two stability index studied earlier by Serre and Zumbrun in order to decide stability

The Perils of `Soft' SUSY Breaking

We consider a two dimensional SU(N) gauge theory coupled to an adjoint Majorana fermion, which is known to be supersymmetric for a particular value of fermion mass. We investigate the `soft' supersymmetry breaking of the discrete light cone quantization (DLCQ) of this theory. There are several DLCQ formulations of this theory currently in the literature and they naively appear to behave differently under `soft' supersymmetry breaking at finite resolution. We show that all these formulations nevertheless yield identical bound state masses in the decompactification limit of the light-like circle. Moreover, we are able to show that the supersymmetry-inspired version of DLCQ (so called `SDLCQ') provides the best rate of convergence of DLCQ bound state masses towards the actual continuum values, except possibly near or at the critical fermion mass. In this last case, we discuss improved extrapolation schemes that must supplement the DLCQ algorithm in order to obtain correct continuum bound state masses. Interestingly, when we truncate the Fock space to two particles, the SDLCQ prescription presented here provides a scheme for improving the rate of convergence of the massive t'Hooft model. Thus the supersymmetry-inspired SDLCQ prescription is applicable to theories without supersymmetry.Comment: 11 pages, Latex; 2 figures (EPS); Numerical results extended; conclusions revise

Deep Sequencing Analysis of RNAs from Citrus Plants Grown in a Citrus Sudden Death-Affected Area Reveals Diverse Known and Putative Novel Viruses.

Citrus sudden death (CSD) has caused the death of approximately four million orange trees in a very important citrus region in Brazil. Although its etiology is still not completely clear, symptoms and distribution of affected plants indicate a viral disease. In a search for viruses associated with CSD, we have performed a comparative high-throughput sequencing analysis of the transcriptome and small RNAs from CSD-symptomatic and -asymptomatic plants using the Illumina platform. The data revealed mixed infections that included Citrus tristeza virus (CTV) as the most predominant virus, followed by the Citrus sudden death-associated virus (CSDaV), Citrus endogenous pararetrovirus (CitPRV) and two putative novel viruses tentatively named Citrus jingmen-like virus (CJLV), and Citrus virga-like virus (CVLV). The deep sequencing analyses were sensitive enough to differentiate two genotypes of both viruses previously associated with CSD-affected plants: CTV and CSDaV. Our data also showed a putative association of the CSD-symptomatic plants with a specific CSDaV genotype and a likely association with CitPRV as well, whereas the two putative novel viruses showed to be more associated with CSD-asymptomatic plants. This is the first high-throughput sequencing-based study of the viral sequences present in CSD-affected citrus plants, and generated valuable information for further CSD studies

Hybrid micro-/nanogels for optical sensing and intracellular imaging

Hybrid micro-/nanogels are playing an increasing important part in a diverse range of applications, due to their tunable dimensions, large surface area, stable interior network structure, and a very short response time. We review recent advances and challenges in the developments of hybrid micro-/nanogels toward applications for optical sensing of pH, temperature, glucose, ions, and other species as well as for intracellular imaging. Due to their unique advantages, hybrid micro-/nanogels as optical probes are attracting substantial interests for continuous monitoring of chemical parameters in complex samples such as blood and bioreactor fluids, in chemical research and industry, and in food quality control. In particular, their intracellular probing ability enables the monitoring of the biochemistry and biophysics of live cells over time and space, thus contributing to the explanation of intricate biological processes and the development of novel diagnoses. Unlike most other probes, hybrid micro-/nanogels could also combine other multiple functions into a single probe. The rational design of hybrid micro-/nanogels will not only improve the probing applications as desirable, but also implement their applications in new arenas. With ongoing rapid advances in bionanotechnology, the well-designed hybrid micro-/nanogel probes will be able to provide simultaneous sensing, imaging diagnosis, and therapy toward clinical applications

Microscopic theory of quadrupolar ordering in TmTe

We have calculated the crystal electric field of TmTe (T>T_Q) and have obtained that the ground state of a Tm 4f hole is the $\Gamma_7$ doublet in agreement with Mossbauer experiments. We study the quadrupole interactions arising from quantum transitions of 4f holes of Tm. An effective attraction is found at the L point of the Brillouin zone, $\vec{q}_L$. Assuming that the quadrupolar condensation involves a single arm of $\vec{q}_L$ we show that there are two variants for quadrupole ordering which are described by the space groups C2/c and C2/m. The Landau free energy is derived in mean-field theory. The phase transition is of second order. The corresponding quadrupole order parameters are combinations of $T_{2g}$ and $E_g$ components. The obtained domain structure is in agreement with observations from neutron diffraction studies for TmTe. Calculated lattice distortions are found to be different for the two variants of quadrupole ordering. We suggest to measure lattice displacements in order to discriminate between those two structures.Comment: 10 pages, 2 figures, 5 tables; accepted by PR