258 research outputs found
Non-real eigenvalues of symmetric Sturm–Liouville problems with indefinite weight functions
On Singularity Formation of a Nonlinear Nonlocal System
We investigate the singularity formation of a nonlinear nonlocal system. This
nonlocal system is a simplified one-dimensional system of the 3D model that was
recently proposed by Hou and Lei in [13] for axisymmetric 3D incompressible
Navier-Stokes equations with swirl. The main difference between the 3D model of
Hou and Lei and the reformulated 3D Navier-Stokes equations is that the
convection term is neglected in the 3D model. In the nonlocal system we
consider in this paper, we replace the Riesz operator in the 3D model by the
Hilbert transform. One of the main results of this paper is that we prove
rigorously the finite time singularity formation of the nonlocal system for a
large class of smooth initial data with finite energy. We also prove the global
regularity for a class of smooth initial data. Numerical results will be
presented to demonstrate the asymptotically self-similar blow-up of the
solution. The blowup rate of the self-similar singularity of the nonlocal
system is similar to that of the 3D model.Comment: 28 pages, 9 figure
Pressure moderation and effective pressure in Navier-Stokes flows
We study the Cauchy problem of the Navier–Stokes equations by both semi-analytic and classical energy methods. The former approach provides a physical picture of how viscous effects may or may not be able to suppress singularity development. In the latter approach, we examine the pressure term that drives the dynamics of the velocity norms ||u||Lq , for q ≥ 3. A key idea behind this investigation is due to the fact that the pressure p in this term is determined upto a function of both space and |u|, say Ƥ(x, |u|), which may assume relatively broad forms. This allows us to use Ƥ as a pressure moderator in the evolution equation for ||u||Lq , whereby optimal regularity criteria can be sought by varying Ƥ within its admissible classes. New regularity criteria are derived with and without making use of the moderator. The results obtained in the absence of the moderator feature some improvement over existing criteria in the literature. Several criteria are derived in terms of the moderated (effective) pressure p+Ƥ. A simple moderation scheme and the plausibility of the present approach to the problem of Navier–Stokes regularity are discussed.PostprintPeer reviewe
A genetic mouse model with postnatal Nf1 and p53 loss recapitulates the histology and transcriptome of human malignant peripheral nerve sheath tumor
BACKGROUND: Malignant peripheral nerve sheath tumors (MPNST) are aggressive sarcomas. Somatic inactivation of
METHODS: We combined 2 genetically modified alleles, an
RESULTS: Postnatal
CONCLUSIONS: The NP-Plp model recapitulates human MPNST genetically, histologically, and molecularly
Radiative Corrections to the Casimir Energy
The lowest radiative correction to the Casimir energy density between two
parallel plates is calculated using effective field theory. Since the
correlators of the electromagnetic field diverge near the plates, the
regularized energy density is also divergent. However, the regularized integral
of the energy density is finite and varies with the plate separation L as
1/L^7. This apparently paradoxical situation is analyzed in an equivalent, but
more transparent theory of a massless scalar field in 1+1 dimensions confined
to a line element of length L and satisfying Dirichlet boundary conditions.Comment: 7 pages, Late
Comparison of arch form between ethnic Malays and Malaysian Aborigines in Peninsular Malaysia
Objective: To determine and compare the frequency distribution of various arch shapes in ethnic Malays and Malaysian Aborigines in Peninsular Malaysia and to investigate the morphological differences of arch form between these two ethnic groups. Methods: We examined 120 ethnic Malay study models (60 maxillary, 60 mandibular) and 129 Malaysian Aboriginal study models (66 maxillary, 63 mandibular). We marked 18 buccal tips and incisor line angles on each model, and digitized them using 2-dimensional coordinate system. Dental arches were classified as square, ovoid, or tapered by printing the scanned images and superimposing Orthoform arch templates on them. Results: The most common maxillary arch shape in both ethnic groups was ovoid, as was the most common mandibular arch shape among ethnic Malay females. The rarest arch shape was square. Chi-square tests, indicated that only the distribution of the mandibular arch shape was significantly different between groups (p = 0.040). However, when compared using independent t-tests, there was no difference in the mean value of arch width between groups. Arch shape distribution was not different between genders of either ethnic group, except for the mandibular arch of ethnic Malays. Conclusions: Ethnic Malays and Malaysian Aborigines have similar dental arch dimensions and shapes. Korean J Orthod 2012;42(1):47-54. This record was migrated from the OpenDepot repository service in June, 2017 before shutting down
Natural radioactivity levels in soils, rocks and water at a mining concession of Perseus gold mine and surrounding towns in Central Region of Ghana
Membraneless organelles formed by liquid-liquid phase separation increase bacterial fitness
Liquid-liquid phase separation is emerging as a crucial phenomenon in several
fundamental cell processes. A range of eukaryotic systems exhibit liquid
condensates. However, their function in bacteria, which in general lack
membrane-bound compartments, remains less clear. Here, we used high-resolution
optical microscopy to observe single bacterial aggresomes, nanostructured
intracellular assemblies of proteins, to undercover their role in cell stress.
We find that proteins inside aggresomes are mobile and undergo dynamic
turnover, consistent with a liquid state. Our observations are in quantitative
agreement with phase-separated liquid droplet formation driven by interacting
proteins under thermal equilibrium that nucleate following diffusive collisions
in the cytoplasm. We have discovered aggresomes in multiple species of
bacteria, and show that these emergent, metastable liquid-structured protein
assemblies increase bacterial fitness by enabling cells to tolerate
environmental stresses
User Oriented Resource Management with Virtualization: A Hierarchical Game Approach
The explosive advancements in mobile Internet and Internet of Things challenge the network capacity and architecture. The ossification of wireless networks hinders the further evolution towards the fifth generation of mobile communication systems. Ultra-dense small cell networks are considered as a feasible way to meet high-capacity demands. Meanwhile, ultradense small cell network virtualization also exploits an insightful perspective for the evolution because of
- …