ON THE ASYMPTOTIC DYNAMICS OF THE VLASOV-YUKAWA-BOLTZMANN SYSTEM NEAR VACUUM

In this pape,~ we study uniform L1-stability and asymptotic completeness of the Vlasov-Yukawa-Boltzmann （V-Y-B） system. For a sufficiently small rand smooth initial data, we show that classical solutions exist globally and satisfy dispersion estimates, uniform L1-stability with respect to initial data and scattering type estimate. We show that the short range nature of interactions due to the Yukawa potential enables us to construct robust Lyapunov type functional to derive scattering states. In the zero mass limit of force carrier particles, we also show that the classical solutions to the V-Y-B system converge to that of the Vlasov-Poisson-Boltzmann （V-P-B） system in any finite time interval

Dynamics of the Austrian Food Market: Application of Lotka-Volterra Differential Equations

The organic food market has become an important part of food industry. We analyze sales data from Austria for 2014 to 2020 of 124 products from 25 product groups in six categories, each in conventional and organic form. We fitted their market shares by means of a modified Lotka-Volterra model with constant coefficients. When only organic and conventional products were compared, a significant increase in market shares was observed for 15 of 25 organic product groups, indicating a continuing growth of the organic food market. The typical Lotka-Volterra dynamics was a predator-prey dynamics with an organic product (group) predating on conventional products that were in symbiosis.

Ungraded Matrix Factorizations as Mirrors of Non-orientable Lagrangians

We introduce the notion of ungraded matrix factorization as a mirror of non-orientable Lagrangian submanifolds.An ungraded matrix factorization of a polynomial W,with coefficients in a field of characteristic 2,is a square matrix Q of polynomial entries satisfying Q^(2)=W·Id.We then show that non-orientable Lagrangians correspond to ungraded matrix factorizations under the localized mirror functor and illustrate this construction in a few instances.Our main example is the Lagrangian submanifold RP^(2)⊂CP^(2)and its mirror ungraded matrix factorization,which we construct and study.In particular,we prove a version of Homological Mirror Symmetry in this setting.

The effect of long-term application of nitrogen-rich fertilizers on soil resistome:A study of conventional and organic cropping systems

Metagenomic studies of various soil environments have previously revealed the widespread distribution of antibiotic resistance genes(ARGs)around the globe.In this study,we applied shotgun metagenomics to investigate differences in microbial communities and resistomes in Chernozem soils that have been under long-term organic and conventional cropping practices.The organic cropping system was seeded with Triticum spelta without any fertilizer.The conventional cropping system was seeded with Tríticum durum Desf and used mineral fertilizer(NPK),that resulted in an increased amount of total and available carbon and nitrogen in soils.Across all samples,we identified a total of 21 ARG classes,among which the dominant were vancomycin,tetracycline and multidrug.Profiling of soil microbial communities revealed differences between the studied fields in the relative abundances of 14 and 53 genera in topsoil and subsoil,respectively.Correlation analysis showed significant correlations(positive and negative)among 18 genera and 6 ARGs,as well as between these ARGs and some chemical properties of soils.The analysis of metagenome-assembled genomes revealed that Nitrospirota,Thermoproteota,Actinobacteriota and Binatota phyla of archaea and bacteria serve as hosts for glycopeptide and fluoroquinolone/tetracycline ARGs.Collectively,the data obtained enrich knowledge about the consequences of human agricultural activities in terms of soil microbiome modification and highlight the role of nitrogen cycling taxa,including uncultivated genera,in the formation of soil resistome.

Approximate Private Quantum Channels on Fermionic Gaussian Systems

The private quantum channel (PQC) maps any quantum state to the maximally mixed state for the discrete as well as the bosonic Gaussian quantum systems, and it has fundamental meaning on the quantum cryptographic tasks and the quantum channel capacity problems. In this paper, we primally introduce a notion of approximate private quantum channel (ε-PQC) on fermionic Gaussian systems (i.e., ε-FPQC), and construct its explicit form of the fermionic (Gaussian) private quantum channel. First of all, we suggest a general structure for ε-FPQC on the fermionic Gaussian systems with respect to the Schatten p-norm class, and then we give an explicit proof of the statement in the trace norm case. In addition, we study that the cardinality of a set of fermionic unitary operators agrees on the ε-FPQC condition in the trace norm case. This result may give birth to intuition on the construction of emerging fermionic Gaussian quantum communication or computing systems.

On the global existence of weak solutions for the Cucker-Smale-Navier-Stokes system with shear thickening

We study the large-time dynamics of Cucker-Smale(C-S)flocking particles interacting with nonNewtonian incompressible fluids.Dynamics of particles and fluids were modeled using the kinetic Cucker-Smale equation for particles and non-Newtonian Navier-Stokes system for fluids,respectively and these two systems are coupled via the drag force,which is the main flocking(alignment)mechanism between particles and fluids.We present a global existence theory for weak solutions to the coupled Cucker-Smale-Navier-Stokes system with shear thickening.We also use a Lyapunov functional approach to show that sufficiently regular solutions approach flocking states exponentially fast in time.

ON FUNCTIONAL TRANSFORMATION OF HYPONORMAL OPERATORS

Let H be a complex separable Hilbert space and L (H) (resp. L_α (H)) be the set of all the linear bounded (resp. bounded self-adjoint) operators on H. For X, Y ∈ L_α (H), let φ, ψ be the bounded real valued Baire functions defined on σ(X) and σ(Y) respectively.

ON AN INEQUALITY OF SEMI-HYPONORMAL OPERATOR SPECTRUM

The operator T=UP on ttilbert space is called ψ-quasi-hyponormal, if it satisfies ψ(P)—U_ψ(P)U=D_ψ≥0. For the invertible ψ-quasi-hyponormal operator T and the scale function ψ satisfying the condition that the function t/ψ(t) is

ON THE ANALYTIC MODEL OF A CLASS OF HYPONORMAL OPERATORS

We consider the singular integrat operator in the Hilbert space L^2[c,d], with the inner

A REPRESENTATION OF NON-ZERO ELEMENTS IN FINITE FIELD

S.W. Colomb proposed the conjecture——there exists a positive integer q_0 such that every non-zero element in GF(q) can be written as a sum of two primitive roots if q>q_0.Such a q_0 has been obtained, but quite large. In this paper we consider whether or not every non-zero element in GF(q) can be written as a sum of two primitive roots for any prime power q=p^n. We will prove that the answer of this question is in the affirmative for one of the following cases: (i) q>6.62×10, and q≠300690391, (ii) n>1 and q≠2~2.If prime power q<10500, the answer of this question is in the negative for q=2, 3, 4, 5,7, 11, 13, 19, 31, 43, 61 and in the affirmative for the others.

Low degree GW invariants of surfaces Ⅱ

We prove a conjectural formula of Maulik-Pandharipande on the degree one and two GW invariants of a surface with a smooth canonical divisor.We use the method of degeneration and the localized GW invariants introduced by the authors.

Uniform boundary Harnack principle for rotationally symmetric Lvy processes in general open sets

In this paper we prove the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous Levy processes.

On Heat Kernel Estimates and Parabolic Harnack Inequality for Jump Processes on Metric Measure Spaces

In this paper, we discuss necessary and sufficient conditions on jumping kernels for a class of jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolic Harnack inequality.

ON THE NON-NORMAL OPERATORS——SEMI-HYPONORMAL OPERATORS

Let A be a linear operator in a Hilbert space H such that Q=（A*A）1/2-（AA*）1/2≥0 andlet A=UR be the polar decomposition. Then there exist opeators A+=lim U*nAUn and A-=lim Un AU*n.In this paper, the relations between the spectra of A+, A-,R and U are derived. Asingular integral model of the operator A is presented. Finally we shall prove the inequality ||Q||≤μφ（σ（A））/2π under certain conditions.

Symmetric Periodic Orbits and Uniruled Real Liouville Domains

A real Liouville domain is a Liouville domain with an exact anti-symplectic involution. The authors call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asymptotically, an invariant finite energy plane converges to a symmetric periodic orbit. In this note, they work out a criterion which guarantees uniruledness for real Liouville domains.