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关键词： Graft transformation   Distance signless Laplacian spectral radius   Non-starlike tree   Non-caterpillar tree  

摘要： Suppose that the vertex set of a connected graph G is V(G) = {v(1), ..., v(n)}. Then we denote by Tr-G(v(i)) the sum of distances between v(i) and all other vertices of G. Let Tr(G) be the n x n diagonal matrix with its (i, i)-entry equal to Tr-G(v(i)) and D(G) be the distance matrix of G. Then Q(D)(G) = Tr(G) + D(G) is the distance signless Laplacian matrix of G. The largest eigenvalues of Q(D)(G) is called distance signless Laplacian spectral radius of G. In this paper we give some graft transformations on distance signless Laplacian spectral radius of the graphs and use them to characterize the graphs with the minimum and maximal distance signless Laplacian spectral radius among non-starlike and non-caterpillar trees.

关键词： Semilinear differential equations   Non-local operators  

摘要： We study semilinear problems in general bounded open sets for non-local operators with exterior and boundary conditions. The operators are more general than the fractional Laplacian. We also give results in case of bounded C-1,C-1 open sets. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Fractional Laplacian   Kirchhoff-type problem   Strong singularity   Uniqueness of solution  

摘要： In this paper, we study the following Kirchhoff-type fractional Laplacian problem with strong singularity:... (a + b similar to u similar to 2)(- similar to)su = f ( x)u-. - k( x)uq in similar to, u > 0 in similar to, u = 0 in R3\ similar to, where (- similar to)s is the fractional Laplace operator, a, b = 0, a + b > 0, similar to is a bounded smooth domain of R3, k. L8 (similar to) is a non-negative function, q. (0, 1),. > 1 and f. L1( similar to) is positive almost everywhere in similar to. Using variational method and Nehari method, we obtain a uniqueness result. A novelty is that the Kirchhoff coefficient may vanish at zero.

关键词： HIV-1   ddPCR   Methods  

摘要： Background: In HIV-1-exposed infants, nucleic acid testing (NAT) is required to diagnose infection since passively transferred maternal antibodies preclude antibody testing. The sensitivity of clinical NAT assays is lowered with infant antiretroviral prophylaxis and, with empiric very early antiretroviral treatment of high-risk infants, thereby impacting early infant diagnosis. Similarly, adult HIV-1 infections acquired under pre-exposure prophylaxis may occur at low levels, with undetectable plasma viremia and indeterminate antibody tests, for which HIV-1 DNA testing maybe a useful adjunct. Cell-associated HIV-1 DNA concentrations are also used to monitor HIV-1 persistence in viral reservoirs with relevance to HIV-1 cure therapeutics, particularly in perinatal infections. Objectives: We clinically validated an HIV-1 DNA quantitative assay using droplet digital PCR (ddPCR), across different HIV-1 subtypes. Study Design: The analytical sensitivity and specificity of an HIV-1 DNA ddPCR assay was determined using serial dilutions of a plasmid containing HIV-1 LTR-gag spiked into peripheral blood mononuclear cells (PBMCs), with MOLT-4 cells or PBMCs infected with different HIV-1 subtypes (A, B and C), and U1 cells spiked into PBMCs. Inter-and intra-run variability were used to determine assay precision. Results: The HIV-1 LTR-gag ddPCR assay was reliable and reproducible, and exhibited high analytical specificity with sensitivity to near single copy level, across multiple HIV-1 subtypes, and a limit of detection of 4.09 copies/ million PBMCs. Conclusions: This assay has applications for detecting occult HIV-1-infection in the setting of combination and long-acting regimens used for HIV-1 prevention, across different HIV-1 subtypes, in infants and adults, and in HIV-1 cure interventions.

关键词： Condensed Matter Physics   Materials Science   general   Atomic   Molecular   Optical and Plasma Physics   Physics   general   Measurement Science and Instrumentation   Classical and Continuum Physics  

摘要： We give a nonequilibrium Green's function (NEGF) perspective on thermodynamics formulations for open quantum systems that are strongly coupled to baths. A scattering approach implying thermodynamic consideration of a supersystem (system plus baths) that is weakly coupled to external superbaths is compared with the consideration of thermodynamics of a system that is strongly coupled to its baths. We analyze both approaches from the NEGF perspective and argue that the latter yields a possibility of thermodynamic formulation consistent with a dynamical (quantum transport) description.

摘要： We study variations of the first nontrivial eigenvalue of the two-dimensional p-Laplace operator, p > 2, generated by measure preserving quasiconformal mappings. The study is based on the geometric theory of composition operators in Sobolev spaces and sharp embedding theorems. Using a sharp version of the reverse Hölder inequality, we obtain a lower estimate for the first nontrivial eigenvalue in the case of Ahlfors type domains. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

关键词： Hamilton inequality   Unbounded Laplacians   Non-degenerated measure   Complete graph   CDE '(-K, infinity)  

摘要： In this paper, we study Hamilton inequality for unbounded Laplacians on weighted graphs satisfying CDE'(-K, infinity) for some K >= 0. This is a generalization of the main result in [8] for bounded Laplacians. For this purpose, we assume a non-degenerated measure and make some modifications to the solutions of the heat equation. As an application of Hamilton inequality, we derive a type of Harnack inequality which compares the heat of two different vertices at the same time. (C) 2021 Published by Elsevier B.V.

关键词： Zinc phthalocyanines   Schiff base   Graphene quantum dots   Photodynamic antimicrobial therapy   S   aureus   Photophysicochemical properties   Antimicrobial photodynamic therapy  

摘要： Antimicrobial resistance is a most important problem facing the treatment of infectious diseases. Antimicrobial photodynamic therapy is an alternative treatment strategy, considered to be cost-effective and feasible. For this purpose, octa-imine substituted ZnPc (3) have been prepared and conjugated to nitrogen, sulfur co-doped graphene quantum dots (N,S-GQDs) through 7C-7C stacking. The photophysical and photochemical properties of Pc alone and and Pc-conjugated to the GQD nanomaterial such as absorption, fluorescence, fluorescence life time, singlet oxygen quantum yields, triplet state quantum yields and exited state lifetimes were investigated in solutions before in vitro cell studies. The PACT activity of prepared structures was investigated against Grampositive (Staphylococcus aureus). Our results suggest that the in the case of conjugation of zinc Pc to N,SGQDs, photodynamic inactivation increased with the 100 % reduction percentage

关键词： dynamics   gluon   general relativity   ricci flow   quantum spinor fields  

摘要： We describe the gluon field dynamics from Unified Spinor Fields, taking into account the quantum self-interactions which come from a Ricci flow in a varied Einstein-Hilbert action. A new action to describe the Yang-Mills fields is introduced and it is obtained the nonlinear equation of motion on a curved background Riemann manifold, with self-interactions included, for the gluon field components.

关键词： Spin waves  

摘要： A finite temperature hydrodynamic model is derived for the spin-1 ultracold bosons by the many-particle quantum hydrodynamic method. It is presented as the two fluid model of the Bose-Einstein condensate (BEC) and normal fluid. The continuity, Euler, spin evolution, and nematic tensor evolution equations are derived for each fluid. The linear and quadratic Zeeman effects are included. Scalar and spin-spin like short-range interactions are considered in the first order by the interaction radius. Obtained hydrodynamic equations are also represented as the set of two nonlinear Pauli equations. The spectrum of the bulk collective excitations is considered for the ferromagnetic phase in the small temperature limit. The spin wave is not affected by the presence of the small temperature in the described minimal coupling model, where the thermal part of the spin-current of the normal fluid is neglected. The two sound waves are affected by the spin evolution in the same way as the change of spectrum of the single sound wave in BEC, where speed of sound is proportional to g 1 + g 2 with g(i) as the interaction constants.